TSTP Solution File: SET662+3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET662+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 : n029.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Apr 30 15:09:56 EDT 2024

% Result   : Theorem 0.14s 0.40s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)

% Comments : 
%------------------------------------------------------------------------------
fof(f304,plain,
    $false,
    inference(resolution,[],[f302,f86]) ).

fof(f86,plain,
    ~ ilf_type(empty_set,relation_type(sK2,sK3)),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,plain,
    ( ~ ilf_type(empty_set,relation_type(sK2,sK3))
    & ilf_type(sK3,set_type)
    & ilf_type(sK2,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f26,f55,f54]) ).

fof(f54,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ~ ilf_type(empty_set,relation_type(X0,X1))
            & ilf_type(X1,set_type) )
        & ilf_type(X0,set_type) )
   => ( ? [X1] :
          ( ~ ilf_type(empty_set,relation_type(sK2,X1))
          & ilf_type(X1,set_type) )
      & ilf_type(sK2,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f55,plain,
    ( ? [X1] :
        ( ~ ilf_type(empty_set,relation_type(sK2,X1))
        & ilf_type(X1,set_type) )
   => ( ~ ilf_type(empty_set,relation_type(sK2,sK3))
      & ilf_type(sK3,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f26,plain,
    ? [X0] :
      ( ? [X1] :
          ( ~ ilf_type(empty_set,relation_type(X0,X1))
          & ilf_type(X1,set_type) )
      & ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f23,negated_conjecture,
    ~ ! [X0] :
        ( ilf_type(X0,set_type)
       => ! [X1] :
            ( ilf_type(X1,set_type)
           => ilf_type(empty_set,relation_type(X0,X1)) ) ),
    inference(negated_conjecture,[],[f22]) ).

fof(f22,conjecture,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ilf_type(empty_set,relation_type(X0,X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_25) ).

fof(f302,plain,
    ! [X0,X1] : ilf_type(empty_set,relation_type(X0,X1)),
    inference(resolution,[],[f289,f143]) ).

fof(f143,plain,
    ! [X3,X0,X1] :
      ( ~ ilf_type(X3,subset_type(cross_product(X0,X1)))
      | ilf_type(X3,relation_type(X0,X1)) ),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102,f133,f105,f134,f135,f106,f136,f137,f107,f138,f139,f109,f140,f141,f108,f142]) ).

fof(f142,plain,
    ! [X3,X0,X1] :
      ( ilf_type(X3,relation_type(X0,X1))
      | ~ ilf_type(X3,subset_type(cross_product(X0,X1)))
      | ~ ilf_type(X1,set_type) ),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102,f133,f105,f134,f135,f106,f136,f137,f107,f138,f139,f109,f140,f141,f108]) ).

fof(f108,plain,
    ! [X3,X0,X1] :
      ( 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(cnf_transformation,[],[f36]) ).

fof(f36,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,[],[f24]) ).

fof(f24,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,[],[f2]) ).

fof(f2,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/sandbox2/benchmark/theBenchmark.p',p2) ).

fof(f141,plain,
    ! [X2,X0,X1] :
      ( ilf_type(X2,subset_type(cross_product(X0,X1)))
      | ~ ilf_type(X2,relation_type(X0,X1)) ),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102,f133,f105,f134,f135,f106,f136,f137,f107,f138,f139,f109,f140]) ).

fof(f140,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) ),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102,f133,f105,f134,f135,f106,f136,f137,f107,f138,f139,f109]) ).

fof(f109,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,[],[f36]) ).

fof(f139,plain,
    ! [X0,X1] : ilf_type(cross_product(X0,X1),set_type),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102,f133,f105,f134,f135,f106,f136,f137,f107,f138]) ).

fof(f138,plain,
    ! [X0,X1] :
      ( ilf_type(cross_product(X0,X1),set_type)
      | ~ ilf_type(X1,set_type) ),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102,f133,f105,f134,f135,f106,f136,f137,f107]) ).

fof(f107,plain,
    ! [X0,X1] :
      ( ilf_type(cross_product(X0,X1),set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ! [X0] :
      ( ! [X1] :
          ( ilf_type(cross_product(X0,X1),set_type)
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ilf_type(cross_product(X0,X1),set_type) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6) ).

fof(f137,plain,
    ! [X0,X1] : ilf_type(ordered_pair(X0,X1),set_type),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102,f133,f105,f134,f135,f106,f136]) ).

fof(f136,plain,
    ! [X0,X1] :
      ( ilf_type(ordered_pair(X0,X1),set_type)
      | ~ ilf_type(X1,set_type) ),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102,f133,f105,f134,f135,f106]) ).

fof(f106,plain,
    ! [X0,X1] :
      ( ilf_type(ordered_pair(X0,X1),set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,plain,
    ! [X0] :
      ( ! [X1] :
          ( ilf_type(ordered_pair(X0,X1),set_type)
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ilf_type(ordered_pair(X0,X1),set_type) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19) ).

fof(f135,plain,
    ! [X0,X1] : subset(empty_set,cross_product(X0,X1)),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102,f133,f105,f134]) ).

fof(f134,plain,
    ! [X0,X1] :
      ( subset(empty_set,cross_product(X0,X1))
      | ~ ilf_type(X1,set_type) ),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102,f133,f105]) ).

fof(f105,plain,
    ! [X0,X1] :
      ( subset(empty_set,cross_product(X0,X1))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X0] :
      ( ! [X1] :
          ( subset(empty_set,cross_product(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(empty_set,cross_product(X0,X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).

fof(f133,plain,
    ! [X2,X0] :
      ( ~ member(X2,X0)
      | ~ ilf_type(X2,set_type)
      | ~ empty(X0) ),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102]) ).

fof(f102,plain,
    ! [X2,X0] :
      ( ~ member(X2,X0)
      | ~ ilf_type(X2,set_type)
      | ~ empty(X0)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f67,plain,
    ! [X0] :
      ( ( ( empty(X0)
          | ( member(sK7(X0),X0)
            & ilf_type(sK7(X0),set_type) ) )
        & ( ! [X2] :
              ( ~ member(X2,X0)
              | ~ ilf_type(X2,set_type) )
          | ~ empty(X0) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f65,f66]) ).

fof(f66,plain,
    ! [X0] :
      ( ? [X1] :
          ( member(X1,X0)
          & ilf_type(X1,set_type) )
     => ( member(sK7(X0),X0)
        & ilf_type(sK7(X0),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f65,plain,
    ! [X0] :
      ( ( ( empty(X0)
          | ? [X1] :
              ( member(X1,X0)
              & ilf_type(X1,set_type) ) )
        & ( ! [X2] :
              ( ~ member(X2,X0)
              | ~ ilf_type(X2,set_type) )
          | ~ empty(X0) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(rectify,[],[f64]) ).

fof(f64,plain,
    ! [X0] :
      ( ( ( empty(X0)
          | ? [X1] :
              ( member(X1,X0)
              & ilf_type(X1,set_type) ) )
        & ( ! [X1] :
              ( ~ member(X1,X0)
              | ~ ilf_type(X1,set_type) )
          | ~ empty(X0) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f32]) ).

fof(f32,plain,
    ! [X0] :
      ( ( empty(X0)
      <=> ! [X1] :
            ( ~ member(X1,X0)
            | ~ ilf_type(X1,set_type) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ( empty(X0)
      <=> ! [X1] :
            ( ilf_type(X1,set_type)
           => ~ member(X1,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p11) ).

fof(f132,plain,
    ! [X0] :
      ( empty(X0)
      | ilf_type(sK7(X0),set_type) ),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103]) ).

fof(f103,plain,
    ! [X0] :
      ( empty(X0)
      | ilf_type(sK7(X0),set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f131,plain,
    ! [X0] :
      ( member(sK7(X0),X0)
      | empty(X0) ),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104]) ).

fof(f104,plain,
    ! [X0] :
      ( empty(X0)
      | member(sK7(X0),X0)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f130,plain,
    ! [X0] : sP1(X0),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101]) ).

fof(f101,plain,
    ! [X0] :
      ( sP1(X0)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f53,plain,
    ! [X0] :
      ( sP1(X0)
      | ~ ilf_type(X0,set_type) ),
    inference(definition_folding,[],[f31,f52,f51]) ).

fof(f51,plain,
    ! [X0] :
      ( sP0(X0)
    <=> ! [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ordered_pair(X2,X3) = X1
                  & ilf_type(X3,set_type) )
              & ilf_type(X2,set_type) )
          | ~ member(X1,X0)
          | ~ ilf_type(X1,set_type) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f52,plain,
    ! [X0] :
      ( ( relation_like(X0)
      <=> sP0(X0) )
      | ~ sP1(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f31,plain,
    ! [X0] :
      ( ( relation_like(X0)
      <=> ! [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ordered_pair(X2,X3) = X1
                    & ilf_type(X3,set_type) )
                & ilf_type(X2,set_type) )
            | ~ member(X1,X0)
            | ~ ilf_type(X1,set_type) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f30]) ).

fof(f30,plain,
    ! [X0] :
      ( ( relation_like(X0)
      <=> ! [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ordered_pair(X2,X3) = X1
                    & ilf_type(X3,set_type) )
                & ilf_type(X2,set_type) )
            | ~ member(X1,X0)
            | ~ ilf_type(X1,set_type) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f17,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ( relation_like(X0)
      <=> ! [X1] :
            ( ilf_type(X1,set_type)
           => ( member(X1,X0)
             => ? [X2] :
                  ( ? [X3] :
                      ( ordered_pair(X2,X3) = X1
                      & ilf_type(X3,set_type) )
                  & ilf_type(X2,set_type) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p16) ).

fof(f95,plain,
    ! [X0,X4] :
      ( ilf_type(sK5(X4),set_type)
      | ~ member(X4,X0)
      | ~ ilf_type(X4,set_type)
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f63,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ( ! [X2] :
              ( ! [X3] :
                  ( ordered_pair(X2,X3) != sK4(X0)
                  | ~ ilf_type(X3,set_type) )
              | ~ ilf_type(X2,set_type) )
          & member(sK4(X0),X0)
          & ilf_type(sK4(X0),set_type) ) )
      & ( ! [X4] :
            ( ( ordered_pair(sK5(X4),sK6(X4)) = X4
              & ilf_type(sK6(X4),set_type)
              & ilf_type(sK5(X4),set_type) )
            | ~ member(X4,X0)
            | ~ ilf_type(X4,set_type) )
        | ~ sP0(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f59,f62,f61,f60]) ).

fof(f60,plain,
    ! [X0] :
      ( ? [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ordered_pair(X2,X3) != X1
                  | ~ ilf_type(X3,set_type) )
              | ~ ilf_type(X2,set_type) )
          & member(X1,X0)
          & ilf_type(X1,set_type) )
     => ( ! [X2] :
            ( ! [X3] :
                ( ordered_pair(X2,X3) != sK4(X0)
                | ~ ilf_type(X3,set_type) )
            | ~ ilf_type(X2,set_type) )
        & member(sK4(X0),X0)
        & ilf_type(sK4(X0),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f61,plain,
    ! [X4] :
      ( ? [X5] :
          ( ? [X6] :
              ( ordered_pair(X5,X6) = X4
              & ilf_type(X6,set_type) )
          & ilf_type(X5,set_type) )
     => ( ? [X6] :
            ( ordered_pair(sK5(X4),X6) = X4
            & ilf_type(X6,set_type) )
        & ilf_type(sK5(X4),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f62,plain,
    ! [X4] :
      ( ? [X6] :
          ( ordered_pair(sK5(X4),X6) = X4
          & ilf_type(X6,set_type) )
     => ( ordered_pair(sK5(X4),sK6(X4)) = X4
        & ilf_type(sK6(X4),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f59,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ? [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ordered_pair(X2,X3) != X1
                    | ~ ilf_type(X3,set_type) )
                | ~ ilf_type(X2,set_type) )
            & member(X1,X0)
            & ilf_type(X1,set_type) ) )
      & ( ! [X4] :
            ( ? [X5] :
                ( ? [X6] :
                    ( ordered_pair(X5,X6) = X4
                    & ilf_type(X6,set_type) )
                & ilf_type(X5,set_type) )
            | ~ member(X4,X0)
            | ~ ilf_type(X4,set_type) )
        | ~ sP0(X0) ) ),
    inference(rectify,[],[f58]) ).

fof(f58,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ? [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ordered_pair(X2,X3) != X1
                    | ~ ilf_type(X3,set_type) )
                | ~ ilf_type(X2,set_type) )
            & member(X1,X0)
            & ilf_type(X1,set_type) ) )
      & ( ! [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ordered_pair(X2,X3) = X1
                    & ilf_type(X3,set_type) )
                & ilf_type(X2,set_type) )
            | ~ member(X1,X0)
            | ~ ilf_type(X1,set_type) )
        | ~ sP0(X0) ) ),
    inference(nnf_transformation,[],[f51]) ).

fof(f96,plain,
    ! [X0,X4] :
      ( ilf_type(sK6(X4),set_type)
      | ~ member(X4,X0)
      | ~ ilf_type(X4,set_type)
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f97,plain,
    ! [X0,X4] :
      ( ordered_pair(sK5(X4),sK6(X4)) = X4
      | ~ member(X4,X0)
      | ~ ilf_type(X4,set_type)
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f98,plain,
    ! [X0] :
      ( sP0(X0)
      | ilf_type(sK4(X0),set_type) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f99,plain,
    ! [X0] :
      ( member(sK4(X0),X0)
      | sP0(X0) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f100,plain,
    ! [X2,X3,X0] :
      ( sP0(X0)
      | ordered_pair(X2,X3) != sK4(X0)
      | ~ ilf_type(X3,set_type)
      | ~ ilf_type(X2,set_type) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f93,plain,
    ! [X0] :
      ( sP0(X0)
      | ~ relation_like(X0)
      | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f57]) ).

fof(f57,plain,
    ! [X0] :
      ( ( ( relation_like(X0)
          | ~ sP0(X0) )
        & ( sP0(X0)
          | ~ relation_like(X0) ) )
      | ~ sP1(X0) ),
    inference(nnf_transformation,[],[f52]) ).

fof(f129,plain,
    ! [X0] : ~ empty(power_set(X0)),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91]) ).

fof(f91,plain,
    ! [X0] :
      ( ~ empty(power_set(X0))
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0] :
      ( ( ilf_type(power_set(X0),set_type)
        & ~ empty(power_set(X0)) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ( ilf_type(power_set(X0),set_type)
        & ~ empty(power_set(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p13) ).

fof(f128,plain,
    ! [X0] : ilf_type(power_set(X0),set_type),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92]) ).

fof(f92,plain,
    ! [X0] :
      ( ilf_type(power_set(X0),set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f127,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89]) ).

fof(f89,plain,
    ! [X0] :
      ( ~ member(X0,empty_set)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0] :
      ( ~ member(X0,empty_set)
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ~ member(X0,empty_set) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).

fof(f88,plain,
    ! [X0] : ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,axiom,
    ! [X0] : ilf_type(X0,set_type),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p20) ).

fof(f87,plain,
    empty(empty_set),
    inference(cnf_transformation,[],[f5]) ).

fof(f5,axiom,
    empty(empty_set),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5a) ).

fof(f84,plain,
    ilf_type(sK2,set_type),
    inference(cnf_transformation,[],[f56]) ).

fof(f85,plain,
    ilf_type(sK3,set_type),
    inference(cnf_transformation,[],[f56]) ).

fof(f289,plain,
    ! [X0] : ilf_type(empty_set,subset_type(X0)),
    inference(resolution,[],[f288,f187]) ).

fof(f187,plain,
    ! [X0] : member(empty_set,power_set(X0)),
    inference(resolution,[],[f156,f127]) ).

fof(f156,plain,
    ! [X0,X1] :
      ( member(sK9(X0,X1),X0)
      | member(X0,power_set(X1)) ),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102,f133,f105,f134,f135,f106,f136,f137,f107,f138,f139,f109,f140,f141,f108,f142,f143,f113,f144,f145,f112,f146,f147,f111,f148,f149,f110,f150,f151,f152,f117,f153,f154,f116,f155]) ).

fof(f155,plain,
    ! [X0,X1] :
      ( member(X0,power_set(X1))
      | member(sK9(X0,X1),X0)
      | ~ ilf_type(X1,set_type) ),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102,f133,f105,f134,f135,f106,f136,f137,f107,f138,f139,f109,f140,f141,f108,f142,f143,f113,f144,f145,f112,f146,f147,f111,f148,f149,f110,f150,f151,f152,f117,f153,f154,f116]) ).

fof(f116,plain,
    ! [X0,X1] :
      ( member(X0,power_set(X1))
      | member(sK9(X0,X1),X0)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f75,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( member(X0,power_set(X1))
              | ( ~ member(sK9(X0,X1),X1)
                & member(sK9(X0,X1),X0)
                & ilf_type(sK9(X0,X1),set_type) ) )
            & ( ! [X3] :
                  ( member(X3,X1)
                  | ~ member(X3,X0)
                  | ~ ilf_type(X3,set_type) )
              | ~ member(X0,power_set(X1)) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f73,f74]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0)
          & ilf_type(X2,set_type) )
     => ( ~ member(sK9(X0,X1),X1)
        & member(sK9(X0,X1),X0)
        & ilf_type(sK9(X0,X1),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f73,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( member(X0,power_set(X1))
              | ? [X2] :
                  ( ~ member(X2,X1)
                  & member(X2,X0)
                  & ilf_type(X2,set_type) ) )
            & ( ! [X3] :
                  ( member(X3,X1)
                  | ~ member(X3,X0)
                  | ~ ilf_type(X3,set_type) )
              | ~ member(X0,power_set(X1)) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(rectify,[],[f72]) ).

fof(f72,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( member(X0,power_set(X1))
              | ? [X2] :
                  ( ~ member(X2,X1)
                  & member(X2,X0)
                  & ilf_type(X2,set_type) ) )
            & ( ! [X2] :
                  ( member(X2,X1)
                  | ~ member(X2,X0)
                  | ~ ilf_type(X2,set_type) )
              | ~ member(X0,power_set(X1)) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f40]) ).

fof(f40,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,[],[f39]) ).

fof(f39,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,[],[f13]) ).

fof(f13,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/sandbox2/benchmark/theBenchmark.p',p12) ).

fof(f154,plain,
    ! [X0,X1] :
      ( ~ member(sK9(X0,X1),X1)
      | member(X0,power_set(X1)) ),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102,f133,f105,f134,f135,f106,f136,f137,f107,f138,f139,f109,f140,f141,f108,f142,f143,f113,f144,f145,f112,f146,f147,f111,f148,f149,f110,f150,f151,f152,f117,f153]) ).

fof(f153,plain,
    ! [X0,X1] :
      ( member(X0,power_set(X1))
      | ~ member(sK9(X0,X1),X1)
      | ~ ilf_type(X1,set_type) ),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102,f133,f105,f134,f135,f106,f136,f137,f107,f138,f139,f109,f140,f141,f108,f142,f143,f113,f144,f145,f112,f146,f147,f111,f148,f149,f110,f150,f151,f152,f117]) ).

fof(f117,plain,
    ! [X0,X1] :
      ( member(X0,power_set(X1))
      | ~ member(sK9(X0,X1),X1)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f152,plain,
    ! [X3,X0,X1] :
      ( ~ member(X3,X0)
      | member(X3,X1)
      | ~ subset(X0,X1) ),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102,f133,f105,f134,f135,f106,f136,f137,f107,f138,f139,f109,f140,f141,f108,f142,f143,f113,f144,f145,f112,f146,f147,f111,f148,f149,f110,f150,f151]) ).

fof(f151,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ ilf_type(X3,set_type)
      | ~ subset(X0,X1) ),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102,f133,f105,f134,f135,f106,f136,f137,f107,f138,f139,f109,f140,f141,f108,f142,f143,f113,f144,f145,f112,f146,f147,f111,f148,f149,f110,f150]) ).

fof(f150,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ ilf_type(X3,set_type)
      | ~ subset(X0,X1)
      | ~ ilf_type(X1,set_type) ),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102,f133,f105,f134,f135,f106,f136,f137,f107,f138,f139,f109,f140,f141,f108,f142,f143,f113,f144,f145,f112,f146,f147,f111,f148,f149,f110]) ).

fof(f110,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ ilf_type(X3,set_type)
      | ~ subset(X0,X1)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f71]) ).

fof(f71,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( subset(X0,X1)
              | ( ~ member(sK8(X0,X1),X1)
                & member(sK8(X0,X1),X0)
                & ilf_type(sK8(X0,X1),set_type) ) )
            & ( ! [X3] :
                  ( member(X3,X1)
                  | ~ member(X3,X0)
                  | ~ ilf_type(X3,set_type) )
              | ~ subset(X0,X1) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f69,f70]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0)
          & ilf_type(X2,set_type) )
     => ( ~ member(sK8(X0,X1),X1)
        & member(sK8(X0,X1),X0)
        & ilf_type(sK8(X0,X1),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f69,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( subset(X0,X1)
              | ? [X2] :
                  ( ~ member(X2,X1)
                  & member(X2,X0)
                  & ilf_type(X2,set_type) ) )
            & ( ! [X3] :
                  ( member(X3,X1)
                  | ~ member(X3,X0)
                  | ~ ilf_type(X3,set_type) )
              | ~ subset(X0,X1) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(rectify,[],[f68]) ).

fof(f68,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( subset(X0,X1)
              | ? [X2] :
                  ( ~ member(X2,X1)
                  & member(X2,X0)
                  & ilf_type(X2,set_type) ) )
            & ( ! [X2] :
                  ( member(X2,X1)
                  | ~ member(X2,X0)
                  | ~ ilf_type(X2,set_type) )
              | ~ subset(X0,X1) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f38]) ).

fof(f38,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,[],[f37]) ).

fof(f37,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,[],[f10]) ).

fof(f10,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/sandbox2/benchmark/theBenchmark.p',p9) ).

fof(f149,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ilf_type(sK8(X0,X1),set_type) ),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102,f133,f105,f134,f135,f106,f136,f137,f107,f138,f139,f109,f140,f141,f108,f142,f143,f113,f144,f145,f112,f146,f147,f111,f148]) ).

fof(f148,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ilf_type(sK8(X0,X1),set_type)
      | ~ ilf_type(X1,set_type) ),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102,f133,f105,f134,f135,f106,f136,f137,f107,f138,f139,f109,f140,f141,f108,f142,f143,f113,f144,f145,f112,f146,f147,f111]) ).

fof(f111,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ilf_type(sK8(X0,X1),set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f71]) ).

fof(f147,plain,
    ! [X0,X1] :
      ( member(sK8(X0,X1),X0)
      | subset(X0,X1) ),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102,f133,f105,f134,f135,f106,f136,f137,f107,f138,f139,f109,f140,f141,f108,f142,f143,f113,f144,f145,f112,f146]) ).

fof(f146,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK8(X0,X1),X0)
      | ~ ilf_type(X1,set_type) ),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102,f133,f105,f134,f135,f106,f136,f137,f107,f138,f139,f109,f140,f141,f108,f142,f143,f113,f144,f145,f112]) ).

fof(f112,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK8(X0,X1),X0)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f71]) ).

fof(f145,plain,
    ! [X0,X1] :
      ( ~ member(sK8(X0,X1),X1)
      | subset(X0,X1) ),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102,f133,f105,f134,f135,f106,f136,f137,f107,f138,f139,f109,f140,f141,f108,f142,f143,f113,f144]) ).

fof(f144,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sK8(X0,X1),X1)
      | ~ ilf_type(X1,set_type) ),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102,f133,f105,f134,f135,f106,f136,f137,f107,f138,f139,f109,f140,f141,f108,f142,f143,f113]) ).

fof(f113,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sK8(X0,X1),X1)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f71]) ).

fof(f288,plain,
    ! [X0,X1] :
      ( ~ member(X0,power_set(X1))
      | ilf_type(X0,subset_type(X1)) ),
    inference(resolution,[],[f287,f163]) ).

fof(f163,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X1,member_type(power_set(X0)))
      | ilf_type(X1,subset_type(X0)) ),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102,f133,f105,f134,f135,f106,f136,f137,f107,f138,f139,f109,f140,f141,f108,f142,f143,f113,f144,f145,f112,f146,f147,f111,f148,f149,f110,f150,f151,f152,f117,f153,f154,f116,f155,f156,f115,f157,f158,f114,f159,f160,f161,f119,f162]) ).

fof(f162,plain,
    ! [X0,X1] :
      ( ilf_type(X1,subset_type(X0))
      | ~ ilf_type(X1,member_type(power_set(X0)))
      | ~ ilf_type(X1,set_type) ),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102,f133,f105,f134,f135,f106,f136,f137,f107,f138,f139,f109,f140,f141,f108,f142,f143,f113,f144,f145,f112,f146,f147,f111,f148,f149,f110,f150,f151,f152,f117,f153,f154,f116,f155,f156,f115,f157,f158,f114,f159,f160,f161,f119]) ).

fof(f119,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(cnf_transformation,[],[f76]) ).

fof(f76,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,[],[f41]) ).

fof(f41,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,[],[f8]) ).

fof(f8,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/sandbox2/benchmark/theBenchmark.p',p7) ).

fof(f161,plain,
    ! [X3,X0,X1] :
      ( ~ member(X0,power_set(X1))
      | ~ member(X3,X0)
      | member(X3,X1) ),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102,f133,f105,f134,f135,f106,f136,f137,f107,f138,f139,f109,f140,f141,f108,f142,f143,f113,f144,f145,f112,f146,f147,f111,f148,f149,f110,f150,f151,f152,f117,f153,f154,f116,f155,f156,f115,f157,f158,f114,f159,f160]) ).

fof(f160,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ ilf_type(X3,set_type)
      | ~ member(X0,power_set(X1)) ),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102,f133,f105,f134,f135,f106,f136,f137,f107,f138,f139,f109,f140,f141,f108,f142,f143,f113,f144,f145,f112,f146,f147,f111,f148,f149,f110,f150,f151,f152,f117,f153,f154,f116,f155,f156,f115,f157,f158,f114,f159]) ).

fof(f159,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ ilf_type(X3,set_type)
      | ~ member(X0,power_set(X1))
      | ~ ilf_type(X1,set_type) ),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102,f133,f105,f134,f135,f106,f136,f137,f107,f138,f139,f109,f140,f141,f108,f142,f143,f113,f144,f145,f112,f146,f147,f111,f148,f149,f110,f150,f151,f152,f117,f153,f154,f116,f155,f156,f115,f157,f158,f114]) ).

fof(f114,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ ilf_type(X3,set_type)
      | ~ member(X0,power_set(X1))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f158,plain,
    ! [X0,X1] :
      ( member(X0,power_set(X1))
      | ilf_type(sK9(X0,X1),set_type) ),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102,f133,f105,f134,f135,f106,f136,f137,f107,f138,f139,f109,f140,f141,f108,f142,f143,f113,f144,f145,f112,f146,f147,f111,f148,f149,f110,f150,f151,f152,f117,f153,f154,f116,f155,f156,f115,f157]) ).

fof(f157,plain,
    ! [X0,X1] :
      ( member(X0,power_set(X1))
      | ilf_type(sK9(X0,X1),set_type)
      | ~ ilf_type(X1,set_type) ),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102,f133,f105,f134,f135,f106,f136,f137,f107,f138,f139,f109,f140,f141,f108,f142,f143,f113,f144,f145,f112,f146,f147,f111,f148,f149,f110,f150,f151,f152,f117,f153,f154,f116,f155,f156,f115]) ).

fof(f115,plain,
    ! [X0,X1] :
      ( member(X0,power_set(X1))
      | ilf_type(sK9(X0,X1),set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f287,plain,
    ! [X0,X1] :
      ( ilf_type(X0,member_type(X1))
      | ~ member(X0,X1) ),
    inference(subsumption_resolution,[],[f286,f176]) ).

fof(f176,plain,
    ! [X2,X0] :
      ( ~ member(X2,X0)
      | ~ empty(X0) ),
    inference(subsumption_resolution,[],[f133,f88]) ).

fof(f286,plain,
    ! [X0,X1] :
      ( ilf_type(X0,member_type(X1))
      | ~ member(X0,X1)
      | empty(X1) ),
    inference(subsumption_resolution,[],[f168,f88]) ).

fof(f168,plain,
    ! [X0,X1] :
      ( ilf_type(X0,member_type(X1))
      | ~ member(X0,X1)
      | empty(X1)
      | ~ ilf_type(X0,set_type) ),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102,f133,f105,f134,f135,f106,f136,f137,f107,f138,f139,f109,f140,f141,f108,f142,f143,f113,f144,f145,f112,f146,f147,f111,f148,f149,f110,f150,f151,f152,f117,f153,f154,f116,f155,f156,f115,f157,f158,f114,f159,f160,f161,f119,f162,f163,f118,f164,f165,f120,f121,f166,f167,f123]) ).

fof(f123,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(cnf_transformation,[],[f79]) ).

fof(f79,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,[],[f45]) ).

fof(f45,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,[],[f44]) ).

fof(f44,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,[],[f15]) ).

fof(f15,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/sandbox2/benchmark/theBenchmark.p',p14) ).

fof(f167,plain,
    ! [X0,X1] : ilf_type(sK10(X0,X1),relation_type(X1,X0)),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102,f133,f105,f134,f135,f106,f136,f137,f107,f138,f139,f109,f140,f141,f108,f142,f143,f113,f144,f145,f112,f146,f147,f111,f148,f149,f110,f150,f151,f152,f117,f153,f154,f116,f155,f156,f115,f157,f158,f114,f159,f160,f161,f119,f162,f163,f118,f164,f165,f120,f121,f166]) ).

fof(f166,plain,
    ! [X0,X1] :
      ( ilf_type(sK10(X0,X1),relation_type(X1,X0))
      | ~ ilf_type(X1,set_type) ),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102,f133,f105,f134,f135,f106,f136,f137,f107,f138,f139,f109,f140,f141,f108,f142,f143,f113,f144,f145,f112,f146,f147,f111,f148,f149,f110,f150,f151,f152,f117,f153,f154,f116,f155,f156,f115,f157,f158,f114,f159,f160,f161,f119,f162,f163,f118,f164,f165,f120,f121]) ).

fof(f121,plain,
    ! [X0,X1] :
      ( ilf_type(sK10(X0,X1),relation_type(X1,X0))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f78]) ).

fof(f78,plain,
    ! [X0] :
      ( ! [X1] :
          ( ilf_type(sK10(X0,X1),relation_type(X1,X0))
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f43,f77]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( ? [X2] : ilf_type(X2,relation_type(X1,X0))
     => ilf_type(sK10(X0,X1),relation_type(X1,X0)) ),
    introduced(choice_axiom,[]) ).

fof(f43,plain,
    ! [X0] :
      ( ! [X1] :
          ( ? [X2] : ilf_type(X2,relation_type(X1,X0))
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ? [X2] : ilf_type(X2,relation_type(X1,X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).

fof(f120,plain,
    ! [X2,X0,X1] :
      ( relation_like(X2)
      | ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f42]) ).

fof(f42,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( relation_like(X2)
              | ~ ilf_type(X2,subset_type(cross_product(X0,X1))) )
          | ~ 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)
         => ! [X2] :
              ( ilf_type(X2,subset_type(cross_product(X0,X1)))
             => relation_like(X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p18) ).

fof(f165,plain,
    ! [X0,X1] :
      ( ilf_type(X1,member_type(power_set(X0)))
      | ~ ilf_type(X1,subset_type(X0)) ),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102,f133,f105,f134,f135,f106,f136,f137,f107,f138,f139,f109,f140,f141,f108,f142,f143,f113,f144,f145,f112,f146,f147,f111,f148,f149,f110,f150,f151,f152,f117,f153,f154,f116,f155,f156,f115,f157,f158,f114,f159,f160,f161,f119,f162,f163,f118,f164]) ).

fof(f164,plain,
    ! [X0,X1] :
      ( ilf_type(X1,member_type(power_set(X0)))
      | ~ ilf_type(X1,subset_type(X0))
      | ~ ilf_type(X1,set_type) ),
    inference(global_subsumption,[],[f86,f85,f84,f87,f88,f89,f127,f92,f128,f91,f129,f93,f100,f99,f98,f97,f96,f95,f101,f130,f104,f131,f103,f132,f102,f133,f105,f134,f135,f106,f136,f137,f107,f138,f139,f109,f140,f141,f108,f142,f143,f113,f144,f145,f112,f146,f147,f111,f148,f149,f110,f150,f151,f152,f117,f153,f154,f116,f155,f156,f115,f157,f158,f114,f159,f160,f161,f119,f162,f163,f118]) ).

fof(f118,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,[],[f76]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SET662+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 : n029.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   : Tue Apr 30 01:35:20 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.37  % (15068)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38  % (15073)WARNING: value z3 for option sas not known
% 0.14/0.38  % (15071)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38  % (15074)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38  % (15073)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  % (15075)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  % (15072)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  % (15076)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  % (15077)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)
% 0.14/0.39  TRYING [1]
% 0.14/0.39  TRYING [2]
% 0.14/0.39  TRYING [3]
% 0.14/0.39  % (15073)First to succeed.
% 0.14/0.39  TRYING [1]
% 0.14/0.40  % (15073)Refutation found. Thanks to Tanya!
% 0.14/0.40  % SZS status Theorem for theBenchmark
% 0.14/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.40  % (15073)------------------------------
% 0.14/0.40  % (15073)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.40  % (15073)Termination reason: Refutation
% 0.14/0.40  
% 0.14/0.40  % (15073)Memory used [KB]: 967
% 0.14/0.40  % (15073)Time elapsed: 0.014 s
% 0.14/0.40  % (15073)Instructions burned: 20 (million)
% 0.14/0.40  % (15073)------------------------------
% 0.14/0.40  % (15073)------------------------------
% 0.14/0.40  % (15068)Success in time 0.03 s
%------------------------------------------------------------------------------