TSTP Solution File: SET656+3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET656+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n022.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 : Sun May  5 09:15:10 EDT 2024

% Result   : Theorem 0.20s 0.43s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   83 (  16 unt;   0 def)
%            Number of atoms       :  316 (  17 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  381 ( 148   ~; 129   |;  54   &)
%                                         (  15 <=>;  35  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   4 con; 0-2 aty)
%            Number of variables   :  173 ( 155   !;  18   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2487,plain,
    $false,
    inference(unit_resulting_resolution,[],[f173,f772,f293]) ).

fof(f293,plain,
    ! [X2,X0,X1] :
      ( ~ ilf_type(X2,relation_type(X0,X1))
      | ilf_type(X2,subset_type(cross_product(X0,X1))) ),
    inference(subsumption_resolution,[],[f292,f175]) ).

fof(f175,plain,
    ! [X0] : ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f30]) ).

fof(f30,axiom,
    ! [X0] : ilf_type(X0,set_type),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p30) ).

fof(f292,plain,
    ! [X2,X0,X1] :
      ( ilf_type(X2,subset_type(cross_product(X0,X1)))
      | ~ ilf_type(X2,relation_type(X0,X1))
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f220,f175]) ).

fof(f220,plain,
    ! [X2,X0,X1] :
      ( ilf_type(X2,subset_type(cross_product(X0,X1)))
      | ~ ilf_type(X2,relation_type(X0,X1))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ! [X2] :
                ( ilf_type(X2,subset_type(cross_product(X0,X1)))
                | ~ ilf_type(X2,relation_type(X0,X1)) )
            & ! [X3] :
                ( ilf_type(X3,relation_type(X0,X1))
                | ~ ilf_type(X3,subset_type(cross_product(X0,X1))) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( ! [X2] :
                ( ilf_type(X2,relation_type(X0,X1))
               => ilf_type(X2,subset_type(cross_product(X0,X1))) )
            & ! [X3] :
                ( ilf_type(X3,subset_type(cross_product(X0,X1)))
               => ilf_type(X3,relation_type(X0,X1)) ) ) ) ),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( ! [X3] :
                ( ilf_type(X3,relation_type(X0,X1))
               => ilf_type(X3,subset_type(cross_product(X0,X1))) )
            & ! [X2] :
                ( ilf_type(X2,subset_type(cross_product(X0,X1)))
               => ilf_type(X2,relation_type(X0,X1)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6) ).

fof(f772,plain,
    ~ ilf_type(sK23,subset_type(cross_product(sK21,sK22))),
    inference(unit_resulting_resolution,[],[f759,f310]) ).

fof(f310,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X1,subset_type(X0))
      | ilf_type(X1,member_type(power_set(X0))) ),
    inference(subsumption_resolution,[],[f309,f175]) ).

fof(f309,plain,
    ! [X0,X1] :
      ( ilf_type(X1,member_type(power_set(X0)))
      | ~ ilf_type(X1,subset_type(X0))
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f246,f175]) ).

fof(f246,plain,
    ! [X0,X1] :
      ( ilf_type(X1,member_type(power_set(X0)))
      | ~ ilf_type(X1,subset_type(X0))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f150]) ).

fof(f150,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( ilf_type(X1,subset_type(X0))
              | ~ ilf_type(X1,member_type(power_set(X0))) )
            & ( ilf_type(X1,member_type(power_set(X0)))
              | ~ ilf_type(X1,subset_type(X0)) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f57]) ).

fof(f57,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ilf_type(X1,subset_type(X0))
          <=> ilf_type(X1,member_type(power_set(X0))) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( ilf_type(X1,subset_type(X0))
          <=> ilf_type(X1,member_type(power_set(X0))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p13) ).

fof(f759,plain,
    ~ ilf_type(sK23,member_type(power_set(cross_product(sK21,sK22)))),
    inference(unit_resulting_resolution,[],[f281,f735,f330]) ).

fof(f330,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X0,member_type(X1))
      | member(X0,X1)
      | empty(X1) ),
    inference(subsumption_resolution,[],[f329,f175]) ).

fof(f329,plain,
    ! [X0,X1] :
      ( member(X0,X1)
      | ~ ilf_type(X0,member_type(X1))
      | empty(X1)
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f267,f175]) ).

fof(f267,plain,
    ! [X0,X1] :
      ( member(X0,X1)
      | ~ ilf_type(X0,member_type(X1))
      | ~ ilf_type(X1,set_type)
      | empty(X1)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f164]) ).

fof(f164,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( ilf_type(X0,member_type(X1))
              | ~ member(X0,X1) )
            & ( member(X0,X1)
              | ~ ilf_type(X0,member_type(X1)) ) )
          | ~ ilf_type(X1,set_type)
          | empty(X1) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f65]) ).

fof(f65,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ilf_type(X0,member_type(X1))
          <=> member(X0,X1) )
          | ~ ilf_type(X1,set_type)
          | empty(X1) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f64]) ).

fof(f64,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ilf_type(X0,member_type(X1))
          <=> member(X0,X1) )
          | ~ ilf_type(X1,set_type)
          | empty(X1) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ( ilf_type(X1,set_type)
            & ~ empty(X1) )
         => ( ilf_type(X0,member_type(X1))
          <=> member(X0,X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21) ).

fof(f735,plain,
    ~ member(sK23,power_set(cross_product(sK21,sK22))),
    inference(unit_resulting_resolution,[],[f476,f306,f239]) ).

fof(f239,plain,
    ! [X0,X1] :
      ( ~ sP16(X0,X1)
      | ~ member(X0,power_set(X1))
      | sP15(X1,X0) ),
    inference(cnf_transformation,[],[f145]) ).

fof(f145,plain,
    ! [X0,X1] :
      ( ( ( member(X0,power_set(X1))
          | ~ sP15(X1,X0) )
        & ( sP15(X1,X0)
          | ~ member(X0,power_set(X1)) ) )
      | ~ sP16(X0,X1) ),
    inference(nnf_transformation,[],[f93]) ).

fof(f93,plain,
    ! [X0,X1] :
      ( ( member(X0,power_set(X1))
      <=> sP15(X1,X0) )
      | ~ sP16(X0,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).

fof(f306,plain,
    ! [X0,X1] : sP16(X0,X1),
    inference(subsumption_resolution,[],[f305,f175]) ).

fof(f305,plain,
    ! [X0,X1] :
      ( sP16(X0,X1)
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f245,f175]) ).

fof(f245,plain,
    ! [X0,X1] :
      ( sP16(X0,X1)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f94]) ).

fof(f94,plain,
    ! [X0] :
      ( ! [X1] :
          ( sP16(X0,X1)
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(definition_folding,[],[f56,f93,f92]) ).

fof(f92,plain,
    ! [X1,X0] :
      ( sP15(X1,X0)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0)
          | ~ ilf_type(X2,set_type) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).

fof(f56,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( member(X0,power_set(X1))
          <=> ! [X2] :
                ( member(X2,X1)
                | ~ member(X2,X0)
                | ~ ilf_type(X2,set_type) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f55]) ).

fof(f55,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( member(X0,power_set(X1))
          <=> ! [X2] :
                ( member(X2,X1)
                | ~ member(X2,X0)
                | ~ ilf_type(X2,set_type) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( member(X0,power_set(X1))
          <=> ! [X2] :
                ( ilf_type(X2,set_type)
               => ( member(X2,X0)
                 => member(X2,X1) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p19) ).

fof(f476,plain,
    ~ sP15(cross_product(sK21,sK22),sK23),
    inference(unit_resulting_resolution,[],[f437,f438,f304]) ).

fof(f304,plain,
    ! [X3,X0,X1] :
      ( ~ sP15(X0,X1)
      | ~ member(X3,X1)
      | member(X3,X0) ),
    inference(subsumption_resolution,[],[f241,f175]) ).

fof(f241,plain,
    ! [X3,X0,X1] :
      ( member(X3,X0)
      | ~ member(X3,X1)
      | ~ ilf_type(X3,set_type)
      | ~ sP15(X0,X1) ),
    inference(cnf_transformation,[],[f149]) ).

fof(f149,plain,
    ! [X0,X1] :
      ( ( sP15(X0,X1)
        | ( ~ member(sK32(X0,X1),X0)
          & member(sK32(X0,X1),X1)
          & ilf_type(sK32(X0,X1),set_type) ) )
      & ( ! [X3] :
            ( member(X3,X0)
            | ~ member(X3,X1)
            | ~ ilf_type(X3,set_type) )
        | ~ sP15(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK32])],[f147,f148]) ).

fof(f148,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X0)
          & member(X2,X1)
          & ilf_type(X2,set_type) )
     => ( ~ member(sK32(X0,X1),X0)
        & member(sK32(X0,X1),X1)
        & ilf_type(sK32(X0,X1),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f147,plain,
    ! [X0,X1] :
      ( ( sP15(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X0)
            & member(X2,X1)
            & ilf_type(X2,set_type) ) )
      & ( ! [X3] :
            ( member(X3,X0)
            | ~ member(X3,X1)
            | ~ ilf_type(X3,set_type) )
        | ~ sP15(X0,X1) ) ),
    inference(rectify,[],[f146]) ).

fof(f146,plain,
    ! [X1,X0] :
      ( ( sP15(X1,X0)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0)
            & ilf_type(X2,set_type) ) )
      & ( ! [X2] :
            ( member(X2,X1)
            | ~ member(X2,X0)
            | ~ ilf_type(X2,set_type) )
        | ~ sP15(X1,X0) ) ),
    inference(nnf_transformation,[],[f92]) ).

fof(f438,plain,
    member(sK31(cross_product(sK21,sK22),sK23),sK23),
    inference(unit_resulting_resolution,[],[f432,f236]) ).

fof(f236,plain,
    ! [X0,X1] :
      ( sP13(X0,X1)
      | member(sK31(X0,X1),X1) ),
    inference(cnf_transformation,[],[f144]) ).

fof(f144,plain,
    ! [X0,X1] :
      ( ( sP13(X0,X1)
        | ( ~ member(sK31(X0,X1),X0)
          & member(sK31(X0,X1),X1)
          & ilf_type(sK31(X0,X1),set_type) ) )
      & ( ! [X3] :
            ( member(X3,X0)
            | ~ member(X3,X1)
            | ~ ilf_type(X3,set_type) )
        | ~ sP13(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK31])],[f142,f143]) ).

fof(f143,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X0)
          & member(X2,X1)
          & ilf_type(X2,set_type) )
     => ( ~ member(sK31(X0,X1),X0)
        & member(sK31(X0,X1),X1)
        & ilf_type(sK31(X0,X1),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f142,plain,
    ! [X0,X1] :
      ( ( sP13(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X0)
            & member(X2,X1)
            & ilf_type(X2,set_type) ) )
      & ( ! [X3] :
            ( member(X3,X0)
            | ~ member(X3,X1)
            | ~ ilf_type(X3,set_type) )
        | ~ sP13(X0,X1) ) ),
    inference(rectify,[],[f141]) ).

fof(f141,plain,
    ! [X1,X0] :
      ( ( sP13(X1,X0)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0)
            & ilf_type(X2,set_type) ) )
      & ( ! [X2] :
            ( member(X2,X1)
            | ~ member(X2,X0)
            | ~ ilf_type(X2,set_type) )
        | ~ sP13(X1,X0) ) ),
    inference(nnf_transformation,[],[f89]) ).

fof(f89,plain,
    ! [X1,X0] :
      ( sP13(X1,X0)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0)
          | ~ ilf_type(X2,set_type) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).

fof(f432,plain,
    ~ sP13(cross_product(sK21,sK22),sK23),
    inference(unit_resulting_resolution,[],[f375,f303,f233]) ).

fof(f233,plain,
    ! [X0,X1] :
      ( ~ sP14(X0,X1)
      | ~ sP13(X1,X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f140]) ).

fof(f140,plain,
    ! [X0,X1] :
      ( ( ( subset(X0,X1)
          | ~ sP13(X1,X0) )
        & ( sP13(X1,X0)
          | ~ subset(X0,X1) ) )
      | ~ sP14(X0,X1) ),
    inference(nnf_transformation,[],[f90]) ).

fof(f90,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
      <=> sP13(X1,X0) )
      | ~ sP14(X0,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).

fof(f303,plain,
    ! [X0,X1] : sP14(X0,X1),
    inference(subsumption_resolution,[],[f302,f175]) ).

fof(f302,plain,
    ! [X0,X1] :
      ( sP14(X0,X1)
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f238,f175]) ).

fof(f238,plain,
    ! [X0,X1] :
      ( sP14(X0,X1)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f91]) ).

fof(f91,plain,
    ! [X0] :
      ( ! [X1] :
          ( sP14(X0,X1)
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(definition_folding,[],[f54,f90,f89]) ).

fof(f54,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( subset(X0,X1)
          <=> ! [X2] :
                ( member(X2,X1)
                | ~ member(X2,X0)
                | ~ ilf_type(X2,set_type) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f53]) ).

fof(f53,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( subset(X0,X1)
          <=> ! [X2] :
                ( member(X2,X1)
                | ~ member(X2,X0)
                | ~ ilf_type(X2,set_type) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f17,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( subset(X0,X1)
          <=> ! [X2] :
                ( ilf_type(X2,set_type)
               => ( member(X2,X0)
                 => member(X2,X1) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p17) ).

fof(f375,plain,
    ~ subset(sK23,cross_product(sK21,sK22)),
    inference(unit_resulting_resolution,[],[f174,f297]) ).

fof(f297,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | intersection(X0,X1) = X0 ),
    inference(subsumption_resolution,[],[f296,f175]) ).

fof(f296,plain,
    ! [X0,X1] :
      ( intersection(X0,X1) = X0
      | ~ subset(X0,X1)
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f221,f175]) ).

fof(f221,plain,
    ! [X0,X1] :
      ( intersection(X0,X1) = X0
      | ~ subset(X0,X1)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f51]) ).

fof(f51,plain,
    ! [X0] :
      ( ! [X1] :
          ( intersection(X0,X1) = X0
          | ~ subset(X0,X1)
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f50]) ).

fof(f50,plain,
    ! [X0] :
      ( ! [X1] :
          ( intersection(X0,X1) = X0
          | ~ subset(X0,X1)
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( subset(X0,X1)
           => intersection(X0,X1) = X0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).

fof(f174,plain,
    sK23 != intersection(sK23,cross_product(sK21,sK22)),
    inference(cnf_transformation,[],[f104]) ).

fof(f104,plain,
    ( sK23 != intersection(sK23,cross_product(sK21,sK22))
    & ilf_type(sK23,relation_type(sK21,sK22))
    & ilf_type(sK22,set_type)
    & ilf_type(sK21,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK21,sK22,sK23])],[f34,f103,f102,f101]) ).

fof(f101,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( intersection(X2,cross_product(X0,X1)) != X2
                & ilf_type(X2,relation_type(X0,X1)) )
            & ilf_type(X1,set_type) )
        & ilf_type(X0,set_type) )
   => ( ? [X1] :
          ( ? [X2] :
              ( intersection(X2,cross_product(sK21,X1)) != X2
              & ilf_type(X2,relation_type(sK21,X1)) )
          & ilf_type(X1,set_type) )
      & ilf_type(sK21,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f102,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( intersection(X2,cross_product(sK21,X1)) != X2
            & ilf_type(X2,relation_type(sK21,X1)) )
        & ilf_type(X1,set_type) )
   => ( ? [X2] :
          ( intersection(X2,cross_product(sK21,sK22)) != X2
          & ilf_type(X2,relation_type(sK21,sK22)) )
      & ilf_type(sK22,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f103,plain,
    ( ? [X2] :
        ( intersection(X2,cross_product(sK21,sK22)) != X2
        & ilf_type(X2,relation_type(sK21,sK22)) )
   => ( sK23 != intersection(sK23,cross_product(sK21,sK22))
      & ilf_type(sK23,relation_type(sK21,sK22)) ) ),
    introduced(choice_axiom,[]) ).

fof(f34,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( intersection(X2,cross_product(X0,X1)) != X2
              & ilf_type(X2,relation_type(X0,X1)) )
          & ilf_type(X1,set_type) )
      & ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f32,negated_conjecture,
    ~ ! [X0] :
        ( ilf_type(X0,set_type)
       => ! [X1] :
            ( ilf_type(X1,set_type)
           => ! [X2] :
                ( ilf_type(X2,relation_type(X0,X1))
               => intersection(X2,cross_product(X0,X1)) = X2 ) ) ),
    inference(negated_conjecture,[],[f31]) ).

fof(f31,conjecture,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,relation_type(X0,X1))
             => intersection(X2,cross_product(X0,X1)) = X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_18) ).

fof(f437,plain,
    ~ member(sK31(cross_product(sK21,sK22),sK23),cross_product(sK21,sK22)),
    inference(unit_resulting_resolution,[],[f432,f237]) ).

fof(f237,plain,
    ! [X0,X1] :
      ( ~ member(sK31(X0,X1),X0)
      | sP13(X0,X1) ),
    inference(cnf_transformation,[],[f144]) ).

fof(f281,plain,
    ! [X0] : ~ empty(power_set(X0)),
    inference(subsumption_resolution,[],[f190,f175]) ).

fof(f190,plain,
    ! [X0] :
      ( ~ empty(power_set(X0))
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,plain,
    ! [X0] :
      ( ( ilf_type(power_set(X0),set_type)
        & ~ empty(power_set(X0)) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ( ilf_type(power_set(X0),set_type)
        & ~ empty(power_set(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p20) ).

fof(f173,plain,
    ilf_type(sK23,relation_type(sK21,sK22)),
    inference(cnf_transformation,[],[f104]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SET656+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36  % Computer : n022.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Fri May  3 16:50:37 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  % (28057)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38  % (28060)WARNING: value z3 for option sas not known
% 0.14/0.38  % (28060)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38  % (28061)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38  % (28059)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38  % (28063)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.38  % (28064)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.38  % (28062)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.38  % (28058)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.39  TRYING [1]
% 0.14/0.39  TRYING [2]
% 0.14/0.40  TRYING [3]
% 0.14/0.41  TRYING [1]
% 0.14/0.42  TRYING [2]
% 0.20/0.42  TRYING [4]
% 0.20/0.42  % (28064)First to succeed.
% 0.20/0.42  % (28064)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-28057"
% 0.20/0.43  % (28064)Refutation found. Thanks to Tanya!
% 0.20/0.43  % SZS status Theorem for theBenchmark
% 0.20/0.43  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.43  % (28064)------------------------------
% 0.20/0.43  % (28064)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.43  % (28064)Termination reason: Refutation
% 0.20/0.43  
% 0.20/0.43  % (28064)Memory used [KB]: 1612
% 0.20/0.43  % (28064)Time elapsed: 0.045 s
% 0.20/0.43  % (28064)Instructions burned: 85 (million)
% 0.20/0.43  % (28057)Success in time 0.062 s
%------------------------------------------------------------------------------