TSTP Solution File: SET155+4 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SET155+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n006.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 : Thu Aug 31 15:06:51 EDT 2023

% Result   : Theorem 190.72s 25.87s
% Output   : CNFRefutation 190.72s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   10
% Syntax   : Number of formulae    :  115 (   8 unt;   0 def)
%            Number of atoms       :  309 (   2 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  337 ( 143   ~; 136   |;  40   &)
%                                         (  11 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-2 aty)
%            Number of variables   :  207 (  15 sgn; 116   !;  12   ?)

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

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

fof(f3,axiom,
    ! [X2,X0] :
      ( member(X2,power_set(X0))
    <=> subset(X2,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_set) ).

fof(f4,axiom,
    ! [X2,X0,X1] :
      ( member(X2,intersection(X0,X1))
    <=> ( member(X2,X1)
        & member(X2,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection) ).

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

fof(f6,axiom,
    ! [X2] : ~ member(X2,empty_set),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).

fof(f7,axiom,
    ! [X1,X0,X3] :
      ( member(X1,difference(X3,X0))
    <=> ( ~ member(X1,X0)
        & member(X1,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference) ).

fof(f12,conjecture,
    ! [X0,X1,X3] :
      ( ( subset(X1,X3)
        & subset(X0,X3) )
     => equal_set(difference(X3,union(X0,X1)),intersection(difference(X3,X0),difference(X3,X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI26) ).

fof(f13,negated_conjecture,
    ~ ! [X0,X1,X3] :
        ( ( subset(X1,X3)
          & subset(X0,X3) )
       => equal_set(difference(X3,union(X0,X1)),intersection(difference(X3,X0),difference(X3,X1))) ),
    inference(negated_conjecture,[],[f12]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( member(X0,power_set(X1))
    <=> subset(X0,X1) ),
    inference(rectify,[],[f3]) ).

fof(f15,plain,
    ! [X0,X1,X2] :
      ( member(X0,intersection(X1,X2))
    <=> ( member(X0,X2)
        & member(X0,X1) ) ),
    inference(rectify,[],[f4]) ).

fof(f16,plain,
    ! [X0,X1,X2] :
      ( member(X0,union(X1,X2))
    <=> ( member(X0,X2)
        | member(X0,X1) ) ),
    inference(rectify,[],[f5]) ).

fof(f17,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(rectify,[],[f6]) ).

fof(f18,plain,
    ! [X0,X1,X2] :
      ( member(X0,difference(X2,X1))
    <=> ( ~ member(X0,X1)
        & member(X0,X2) ) ),
    inference(rectify,[],[f7]) ).

fof(f23,plain,
    ~ ! [X0,X1,X2] :
        ( ( subset(X1,X2)
          & subset(X0,X2) )
       => equal_set(difference(X2,union(X0,X1)),intersection(difference(X2,X0),difference(X2,X1))) ),
    inference(rectify,[],[f13]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ( subset(X1,X0)
        & subset(X0,X1) )
     => equal_set(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f2]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(flattening,[],[f26]) ).

fof(f29,plain,
    ? [X0,X1,X2] :
      ( ~ equal_set(difference(X2,union(X0,X1)),intersection(difference(X2,X0),difference(X2,X1)))
      & subset(X1,X2)
      & subset(X0,X2) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f30,plain,
    ? [X0,X1,X2] :
      ( ~ equal_set(difference(X2,union(X0,X1)),intersection(difference(X2,X0),difference(X2,X1)))
      & subset(X1,X2)
      & subset(X0,X2) ),
    inference(flattening,[],[f29]) ).

fof(f31,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,[],[f25]) ).

fof(f32,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,[],[f31]) ).

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

fof(f34,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])],[f32,f33]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ( member(X0,power_set(X1))
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ~ member(X0,power_set(X1)) ) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f36,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,intersection(X1,X2))
        | ~ member(X0,X2)
        | ~ member(X0,X1) )
      & ( ( member(X0,X2)
          & member(X0,X1) )
        | ~ member(X0,intersection(X1,X2)) ) ),
    inference(nnf_transformation,[],[f15]) ).

fof(f37,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,intersection(X1,X2))
        | ~ member(X0,X2)
        | ~ member(X0,X1) )
      & ( ( member(X0,X2)
          & member(X0,X1) )
        | ~ member(X0,intersection(X1,X2)) ) ),
    inference(flattening,[],[f36]) ).

fof(f38,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,union(X1,X2))
        | ( ~ member(X0,X2)
          & ~ member(X0,X1) ) )
      & ( member(X0,X2)
        | member(X0,X1)
        | ~ member(X0,union(X1,X2)) ) ),
    inference(nnf_transformation,[],[f16]) ).

fof(f39,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,union(X1,X2))
        | ( ~ member(X0,X2)
          & ~ member(X0,X1) ) )
      & ( member(X0,X2)
        | member(X0,X1)
        | ~ member(X0,union(X1,X2)) ) ),
    inference(flattening,[],[f38]) ).

fof(f40,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,difference(X2,X1))
        | member(X0,X1)
        | ~ member(X0,X2) )
      & ( ( ~ member(X0,X1)
          & member(X0,X2) )
        | ~ member(X0,difference(X2,X1)) ) ),
    inference(nnf_transformation,[],[f18]) ).

fof(f41,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,difference(X2,X1))
        | member(X0,X1)
        | ~ member(X0,X2) )
      & ( ( ~ member(X0,X1)
          & member(X0,X2) )
        | ~ member(X0,difference(X2,X1)) ) ),
    inference(flattening,[],[f40]) ).

fof(f53,plain,
    ( ? [X0,X1,X2] :
        ( ~ equal_set(difference(X2,union(X0,X1)),intersection(difference(X2,X0),difference(X2,X1)))
        & subset(X1,X2)
        & subset(X0,X2) )
   => ( ~ equal_set(difference(sK5,union(sK3,sK4)),intersection(difference(sK5,sK3),difference(sK5,sK4)))
      & subset(sK4,sK5)
      & subset(sK3,sK5) ) ),
    introduced(choice_axiom,[]) ).

fof(f54,plain,
    ( ~ equal_set(difference(sK5,union(sK3,sK4)),intersection(difference(sK5,sK3),difference(sK5,sK4)))
    & subset(sK4,sK5)
    & subset(sK3,sK5) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f30,f53]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK0(X0,X1),X0) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(X0,power_set(X1)) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( member(X0,power_set(X1))
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f61,plain,
    ! [X2,X0,X1] :
      ( member(X0,X1)
      | ~ member(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f62,plain,
    ! [X2,X0,X1] :
      ( member(X0,X2)
      | ~ member(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f63,plain,
    ! [X2,X0,X1] :
      ( member(X0,intersection(X1,X2))
      | ~ member(X0,X2)
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f64,plain,
    ! [X2,X0,X1] :
      ( member(X0,X2)
      | member(X0,X1)
      | ~ member(X0,union(X1,X2)) ),
    inference(cnf_transformation,[],[f39]) ).

fof(f65,plain,
    ! [X2,X0,X1] :
      ( member(X0,union(X1,X2))
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[],[f39]) ).

fof(f66,plain,
    ! [X2,X0,X1] :
      ( member(X0,union(X1,X2))
      | ~ member(X0,X2) ),
    inference(cnf_transformation,[],[f39]) ).

fof(f67,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(cnf_transformation,[],[f17]) ).

fof(f68,plain,
    ! [X2,X0,X1] :
      ( member(X0,X2)
      | ~ member(X0,difference(X2,X1)) ),
    inference(cnf_transformation,[],[f41]) ).

fof(f69,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,X1)
      | ~ member(X0,difference(X2,X1)) ),
    inference(cnf_transformation,[],[f41]) ).

fof(f70,plain,
    ! [X2,X0,X1] :
      ( member(X0,difference(X2,X1))
      | member(X0,X1)
      | ~ member(X0,X2) ),
    inference(cnf_transformation,[],[f41]) ).

fof(f84,plain,
    ~ equal_set(difference(sK5,union(sK3,sK4)),intersection(difference(sK5,sK3),difference(sK5,sK4))),
    inference(cnf_transformation,[],[f54]) ).

cnf(c_49,plain,
    ( ~ member(sK0(X0,X1),X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f57]) ).

cnf(c_50,plain,
    ( member(sK0(X0,X1),X0)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f56]) ).

cnf(c_52,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X1,X0)
    | equal_set(X0,X1) ),
    inference(cnf_transformation,[],[f58]) ).

cnf(c_53,plain,
    ( ~ subset(X0,X1)
    | member(X0,power_set(X1)) ),
    inference(cnf_transformation,[],[f60]) ).

cnf(c_54,plain,
    ( ~ member(X0,power_set(X1))
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f59]) ).

cnf(c_55,plain,
    ( ~ member(X0,X1)
    | ~ member(X0,X2)
    | member(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[],[f63]) ).

cnf(c_56,plain,
    ( ~ member(X0,intersection(X1,X2))
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f62]) ).

cnf(c_57,plain,
    ( ~ member(X0,intersection(X1,X2))
    | member(X0,X1) ),
    inference(cnf_transformation,[],[f61]) ).

cnf(c_58,plain,
    ( ~ member(X0,X1)
    | member(X0,union(X2,X1)) ),
    inference(cnf_transformation,[],[f66]) ).

cnf(c_59,plain,
    ( ~ member(X0,X1)
    | member(X0,union(X1,X2)) ),
    inference(cnf_transformation,[],[f65]) ).

cnf(c_60,plain,
    ( ~ member(X0,union(X1,X2))
    | member(X0,X1)
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f64]) ).

cnf(c_61,plain,
    ~ member(X0,empty_set),
    inference(cnf_transformation,[],[f67]) ).

cnf(c_62,plain,
    ( ~ member(X0,X1)
    | member(X0,difference(X1,X2))
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f70]) ).

cnf(c_63,plain,
    ( ~ member(X0,difference(X1,X2))
    | ~ member(X0,X2) ),
    inference(cnf_transformation,[],[f69]) ).

cnf(c_64,plain,
    ( ~ member(X0,difference(X1,X2))
    | member(X0,X1) ),
    inference(cnf_transformation,[],[f68]) ).

cnf(c_76,negated_conjecture,
    ~ equal_set(difference(sK5,union(sK3,sK4)),intersection(difference(sK5,sK3),difference(sK5,sK4))),
    inference(cnf_transformation,[],[f84]) ).

cnf(c_331,plain,
    ( intersection(difference(sK5,sK3),difference(sK5,sK4)) != X1
    | difference(sK5,union(sK3,sK4)) != X0
    | ~ subset(X0,X1)
    | ~ subset(X1,X0) ),
    inference(resolution_lifted,[status(thm)],[c_52,c_76]) ).

cnf(c_332,plain,
    ( ~ subset(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4)))
    | ~ subset(difference(sK5,union(sK3,sK4)),intersection(difference(sK5,sK3),difference(sK5,sK4))) ),
    inference(unflattening,[status(thm)],[c_331]) ).

cnf(c_1225,plain,
    ( ~ member(sK0(difference(sK5,union(sK3,sK4)),intersection(difference(sK5,sK3),difference(sK5,sK4))),intersection(difference(sK5,sK3),difference(sK5,sK4)))
    | subset(difference(sK5,union(sK3,sK4)),intersection(difference(sK5,sK3),difference(sK5,sK4))) ),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_1538,plain,
    ( member(sK0(difference(sK5,union(sK3,sK4)),intersection(difference(sK5,sK3),difference(sK5,sK4))),difference(sK5,union(sK3,sK4)))
    | subset(difference(sK5,union(sK3,sK4)),intersection(difference(sK5,sK3),difference(sK5,sK4))) ),
    inference(instantiation,[status(thm)],[c_50]) ).

cnf(c_1845,plain,
    ( ~ member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),difference(sK5,union(sK3,sK4)))
    | subset(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))) ),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_1846,plain,
    ( ~ member(intersection(difference(sK5,sK3),difference(sK5,sK4)),power_set(difference(sK5,union(sK3,sK4))))
    | subset(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))) ),
    inference(instantiation,[status(thm)],[c_54]) ).

cnf(c_2718,plain,
    ( ~ subset(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4)))
    | member(intersection(difference(sK5,sK3),difference(sK5,sK4)),power_set(difference(sK5,union(sK3,sK4)))) ),
    inference(instantiation,[status(thm)],[c_53]) ).

cnf(c_7749,plain,
    ( member(sK0(X0,difference(sK5,union(sK3,sK4))),X0)
    | subset(X0,difference(sK5,union(sK3,sK4))) ),
    inference(instantiation,[status(thm)],[c_50]) ).

cnf(c_13832,plain,
    ( member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),intersection(difference(sK5,sK3),difference(sK5,sK4)))
    | subset(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))) ),
    inference(instantiation,[status(thm)],[c_7749]) ).

cnf(c_454473,plain,
    ( ~ member(X0,power_set(X1))
    | member(X0,union(power_set(X1),X2)) ),
    inference(instantiation,[status(thm)],[c_59]) ).

cnf(c_454582,plain,
    ( ~ member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),intersection(difference(sK5,sK3),difference(sK5,sK4)))
    | ~ member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),X0)
    | member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),intersection(X0,intersection(difference(sK5,sK3),difference(sK5,sK4)))) ),
    inference(instantiation,[status(thm)],[c_55]) ).

cnf(c_454584,plain,
    ( ~ member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),intersection(difference(sK5,sK3),difference(sK5,sK4)))
    | member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),difference(sK5,sK3)) ),
    inference(instantiation,[status(thm)],[c_57]) ).

cnf(c_454585,plain,
    ( ~ member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),intersection(difference(sK5,sK3),difference(sK5,sK4)))
    | member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),difference(sK5,sK4)) ),
    inference(instantiation,[status(thm)],[c_56]) ).

cnf(c_454791,plain,
    ( ~ member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),difference(sK5,sK3))
    | ~ member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),sK3) ),
    inference(instantiation,[status(thm)],[c_63]) ).

cnf(c_454838,plain,
    ( ~ member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),difference(sK5,sK4))
    | member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),sK5) ),
    inference(instantiation,[status(thm)],[c_64]) ).

cnf(c_454839,plain,
    ( ~ member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),difference(sK5,sK4))
    | ~ member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),sK4) ),
    inference(instantiation,[status(thm)],[c_63]) ).

cnf(c_455047,plain,
    ( ~ member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),union(X0,X1))
    | member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),X0)
    | member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),X1) ),
    inference(instantiation,[status(thm)],[c_60]) ).

cnf(c_457636,plain,
    ( ~ member(intersection(difference(sK5,sK3),difference(sK5,sK4)),power_set(difference(sK5,union(sK3,sK4))))
    | member(intersection(difference(sK5,sK3),difference(sK5,sK4)),union(power_set(difference(sK5,union(sK3,sK4))),X0)) ),
    inference(instantiation,[status(thm)],[c_454473]) ).

cnf(c_458660,plain,
    ( ~ member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),union(X0,sK4))
    | member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),X0)
    | member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),sK4) ),
    inference(instantiation,[status(thm)],[c_455047]) ).

cnf(c_463127,plain,
    ( ~ member(X0,union(X1,empty_set))
    | member(X0,X1)
    | member(X0,empty_set) ),
    inference(instantiation,[status(thm)],[c_60]) ).

cnf(c_464270,plain,
    ( ~ member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),intersection(difference(sK5,sK3),difference(sK5,sK4)))
    | ~ member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),sK3)
    | member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),intersection(sK3,intersection(difference(sK5,sK3),difference(sK5,sK4)))) ),
    inference(instantiation,[status(thm)],[c_454582]) ).

cnf(c_464445,plain,
    ( ~ member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),intersection(difference(sK5,sK3),difference(sK5,sK4)))
    | ~ member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),sK4)
    | member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),intersection(sK4,intersection(difference(sK5,sK3),difference(sK5,sK4)))) ),
    inference(instantiation,[status(thm)],[c_454582]) ).

cnf(c_464985,plain,
    ( member(X0,X1)
    | ~ member(X0,union(X1,empty_set)) ),
    inference(global_subsumption_just,[status(thm)],[c_463127,c_61,c_463127]) ).

cnf(c_464986,plain,
    ( ~ member(X0,union(X1,empty_set))
    | member(X0,X1) ),
    inference(renaming,[status(thm)],[c_464985]) ).

cnf(c_464997,plain,
    ( ~ member(intersection(difference(sK5,sK3),difference(sK5,sK4)),union(power_set(difference(sK5,union(sK3,sK4))),empty_set))
    | member(intersection(difference(sK5,sK3),difference(sK5,sK4)),power_set(difference(sK5,union(sK3,sK4)))) ),
    inference(instantiation,[status(thm)],[c_464986]) ).

cnf(c_466583,plain,
    ( ~ member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),union(sK3,sK4))
    | member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),sK3)
    | member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),sK4) ),
    inference(instantiation,[status(thm)],[c_458660]) ).

cnf(c_469203,plain,
    ( ~ member(sK0(X0,X1),X2)
    | member(sK0(X0,X1),difference(X2,X3))
    | member(sK0(X0,X1),X3) ),
    inference(instantiation,[status(thm)],[c_62]) ).

cnf(c_469207,plain,
    ( ~ member(sK0(X0,X1),X2)
    | ~ member(sK0(X0,X1),X3)
    | member(sK0(X0,X1),intersection(X2,X3)) ),
    inference(instantiation,[status(thm)],[c_55]) ).

cnf(c_469210,plain,
    ( ~ member(sK0(X0,X1),X2)
    | member(sK0(X0,X1),union(X3,X2)) ),
    inference(instantiation,[status(thm)],[c_58]) ).

cnf(c_470729,plain,
    ( ~ member(X0,difference(X1,difference(X2,X3)))
    | member(X0,X1) ),
    inference(instantiation,[status(thm)],[c_64]) ).

cnf(c_472800,plain,
    ( ~ member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),sK3)
    | ~ member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),intersection(difference(sK5,sK3),difference(sK5,sK4))) ),
    inference(global_subsumption_just,[status(thm)],[c_464270,c_454584,c_454791]) ).

cnf(c_472801,plain,
    ( ~ member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),intersection(difference(sK5,sK3),difference(sK5,sK4)))
    | ~ member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),sK3) ),
    inference(renaming,[status(thm)],[c_472800]) ).

cnf(c_472938,plain,
    ( ~ member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),sK4)
    | ~ member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),intersection(difference(sK5,sK3),difference(sK5,sK4))) ),
    inference(global_subsumption_just,[status(thm)],[c_464445,c_454585,c_454839]) ).

cnf(c_472939,plain,
    ( ~ member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),intersection(difference(sK5,sK3),difference(sK5,sK4)))
    | ~ member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),sK4) ),
    inference(renaming,[status(thm)],[c_472938]) ).

cnf(c_473228,plain,
    ( ~ member(sK0(X0,X1),X2)
    | member(sK0(X0,X1),union(X2,X3)) ),
    inference(instantiation,[status(thm)],[c_59]) ).

cnf(c_476228,plain,
    ( ~ member(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(union(power_set(difference(sK5,union(sK3,sK4))),empty_set),difference(X0,X1)))
    | member(intersection(difference(sK5,sK3),difference(sK5,sK4)),union(power_set(difference(sK5,union(sK3,sK4))),empty_set)) ),
    inference(instantiation,[status(thm)],[c_470729]) ).

cnf(c_477228,plain,
    ( ~ member(intersection(difference(sK5,sK3),difference(sK5,sK4)),power_set(difference(sK5,union(sK3,sK4))))
    | member(intersection(difference(sK5,sK3),difference(sK5,sK4)),union(power_set(difference(sK5,union(sK3,sK4))),empty_set)) ),
    inference(instantiation,[status(thm)],[c_457636]) ).

cnf(c_485028,plain,
    ( ~ member(sK0(difference(sK5,union(sK3,sK4)),intersection(difference(sK5,sK3),difference(sK5,sK4))),difference(sK5,union(sK3,sK4)))
    | member(sK0(difference(sK5,union(sK3,sK4)),intersection(difference(sK5,sK3),difference(sK5,sK4))),sK5) ),
    inference(instantiation,[status(thm)],[c_64]) ).

cnf(c_485029,plain,
    ( ~ member(sK0(difference(sK5,union(sK3,sK4)),intersection(difference(sK5,sK3),difference(sK5,sK4))),difference(sK5,union(sK3,sK4)))
    | ~ member(sK0(difference(sK5,union(sK3,sK4)),intersection(difference(sK5,sK3),difference(sK5,sK4))),union(sK3,sK4)) ),
    inference(instantiation,[status(thm)],[c_63]) ).

cnf(c_505023,plain,
    ( ~ member(sK0(difference(sK5,union(sK3,sK4)),intersection(difference(sK5,sK3),difference(sK5,sK4))),sK4)
    | member(sK0(difference(sK5,union(sK3,sK4)),intersection(difference(sK5,sK3),difference(sK5,sK4))),union(sK3,sK4)) ),
    inference(instantiation,[status(thm)],[c_469210]) ).

cnf(c_506570,plain,
    ( ~ member(sK0(difference(sK5,union(sK3,sK4)),intersection(difference(sK5,sK3),difference(sK5,sK4))),sK3)
    | member(sK0(difference(sK5,union(sK3,sK4)),intersection(difference(sK5,sK3),difference(sK5,sK4))),union(sK3,sK4)) ),
    inference(instantiation,[status(thm)],[c_473228]) ).

cnf(c_508378,plain,
    ( ~ member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),sK5)
    | member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),difference(sK5,union(sK3,sK4)))
    | member(sK0(intersection(difference(sK5,sK3),difference(sK5,sK4)),difference(sK5,union(sK3,sK4))),union(sK3,sK4)) ),
    inference(instantiation,[status(thm)],[c_469203]) ).

cnf(c_509401,plain,
    member(intersection(difference(sK5,sK3),difference(sK5,sK4)),union(power_set(difference(sK5,union(sK3,sK4))),empty_set)),
    inference(global_subsumption_just,[status(thm)],[c_476228,c_1845,c_2718,c_13832,c_454585,c_454838,c_466583,c_472801,c_472939,c_477228,c_508378]) ).

cnf(c_519644,plain,
    ( ~ member(sK0(difference(sK5,union(sK3,sK4)),intersection(difference(sK5,sK3),difference(sK5,sK4))),X0)
    | member(sK0(difference(sK5,union(sK3,sK4)),intersection(difference(sK5,sK3),difference(sK5,sK4))),difference(X0,sK4))
    | member(sK0(difference(sK5,union(sK3,sK4)),intersection(difference(sK5,sK3),difference(sK5,sK4))),sK4) ),
    inference(instantiation,[status(thm)],[c_469203]) ).

cnf(c_519645,plain,
    ( ~ member(sK0(difference(sK5,union(sK3,sK4)),intersection(difference(sK5,sK3),difference(sK5,sK4))),sK5)
    | member(sK0(difference(sK5,union(sK3,sK4)),intersection(difference(sK5,sK3),difference(sK5,sK4))),difference(sK5,sK4))
    | member(sK0(difference(sK5,union(sK3,sK4)),intersection(difference(sK5,sK3),difference(sK5,sK4))),sK4) ),
    inference(instantiation,[status(thm)],[c_519644]) ).

cnf(c_519646,plain,
    ( ~ member(sK0(difference(sK5,union(sK3,sK4)),intersection(difference(sK5,sK3),difference(sK5,sK4))),X0)
    | member(sK0(difference(sK5,union(sK3,sK4)),intersection(difference(sK5,sK3),difference(sK5,sK4))),difference(X0,sK3))
    | member(sK0(difference(sK5,union(sK3,sK4)),intersection(difference(sK5,sK3),difference(sK5,sK4))),sK3) ),
    inference(instantiation,[status(thm)],[c_469203]) ).

cnf(c_519647,plain,
    ( ~ member(sK0(difference(sK5,union(sK3,sK4)),intersection(difference(sK5,sK3),difference(sK5,sK4))),sK5)
    | member(sK0(difference(sK5,union(sK3,sK4)),intersection(difference(sK5,sK3),difference(sK5,sK4))),difference(sK5,sK3))
    | member(sK0(difference(sK5,union(sK3,sK4)),intersection(difference(sK5,sK3),difference(sK5,sK4))),sK3) ),
    inference(instantiation,[status(thm)],[c_519646]) ).

cnf(c_522818,plain,
    ( ~ member(sK0(difference(sK5,union(sK3,sK4)),intersection(difference(sK5,sK3),difference(sK5,sK4))),difference(sK5,sK3))
    | ~ member(sK0(difference(sK5,union(sK3,sK4)),intersection(difference(sK5,sK3),difference(sK5,sK4))),difference(sK5,sK4))
    | member(sK0(difference(sK5,union(sK3,sK4)),intersection(difference(sK5,sK3),difference(sK5,sK4))),intersection(difference(sK5,sK3),difference(sK5,sK4))) ),
    inference(instantiation,[status(thm)],[c_469207]) ).

cnf(c_522819,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_522818,c_519647,c_519645,c_509401,c_506570,c_505023,c_485028,c_485029,c_464997,c_1846,c_1538,c_1225,c_332]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET155+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n006.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Sat Aug 26 15:20:52 EDT 2023
% 0.13/0.35  % 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 --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 190.72/25.87  % SZS status Started for theBenchmark.p
% 190.72/25.87  % SZS status Theorem for theBenchmark.p
% 190.72/25.87  
% 190.72/25.87  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 190.72/25.87  
% 190.72/25.87  ------  iProver source info
% 190.72/25.87  
% 190.72/25.87  git: date: 2023-05-31 18:12:56 +0000
% 190.72/25.87  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 190.72/25.87  git: non_committed_changes: false
% 190.72/25.87  git: last_make_outside_of_git: false
% 190.72/25.87  
% 190.72/25.87  ------ Parsing...
% 190.72/25.87  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 190.72/25.87  
% 190.72/25.87  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e 
% 190.72/25.87  
% 190.72/25.87  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 190.72/25.87  
% 190.72/25.87  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 190.72/25.87  ------ Proving...
% 190.72/25.87  ------ Problem Properties 
% 190.72/25.87  
% 190.72/25.87  
% 190.72/25.87  clauses                                 29
% 190.72/25.87  conjectures                             2
% 190.72/25.87  EPR                                     4
% 190.72/25.87  Horn                                    24
% 190.72/25.87  unary                                   6
% 190.72/25.87  binary                                  16
% 190.72/25.87  lits                                    59
% 190.72/25.87  lits eq                                 3
% 190.72/25.87  fd_pure                                 0
% 190.72/25.87  fd_pseudo                               0
% 190.72/25.87  fd_cond                                 0
% 190.72/25.87  fd_pseudo_cond                          2
% 190.72/25.87  AC symbols                              0
% 190.72/25.87  
% 190.72/25.87  ------ Input Options Time Limit: Unbounded
% 190.72/25.87  
% 190.72/25.87  
% 190.72/25.87  ------ 
% 190.72/25.87  Current options:
% 190.72/25.87  ------ 
% 190.72/25.87  
% 190.72/25.87  
% 190.72/25.87  
% 190.72/25.87  
% 190.72/25.87  ------ Proving...
% 190.72/25.87  
% 190.72/25.87  
% 190.72/25.87  ------ Proving...
% 190.72/25.87  
% 190.72/25.87  
% 190.72/25.87  ------ Proving...
% 190.72/25.87  
% 190.72/25.87  
% 190.72/25.87  ------ Proving...
% 190.72/25.87  
% 190.72/25.87  
% 190.72/25.87  ------ Proving...
% 190.72/25.87  
% 190.72/25.87  
% 190.72/25.87  ------ Proving...
% 190.72/25.87  
% 190.72/25.87  
% 190.72/25.87  ------ Proving...
% 190.72/25.87  
% 190.72/25.87  
% 190.72/25.87  ------ Proving...
% 190.72/25.87  
% 190.72/25.87  
% 190.72/25.87  ------ Proving...
% 190.72/25.87  
% 190.72/25.87  
% 190.72/25.87  ------ Proving...
% 190.72/25.87  
% 190.72/25.87  
% 190.72/25.87  ------ Proving...
% 190.72/25.87  
% 190.72/25.87  
% 190.72/25.87  % SZS status Theorem for theBenchmark.p
% 190.72/25.87  
% 190.72/25.87  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 190.72/25.87  
% 190.72/25.87  
%------------------------------------------------------------------------------