TSTP Solution File: SET656+3 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET656+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s

% Computer : n016.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 : Wed Aug 31 18:25:15 EDT 2022

% Result   : Theorem 1.49s 0.55s
% Output   : Refutation 1.49s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   83 (  16 unt;   0 def)
%            Number of atoms       :  330 (  23 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  408 ( 161   ~; 153   |;  52   &)
%                                         (  11 <=>;  31  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;   7 con; 0-2 aty)
%            Number of variables   :  158 ( 140   !;  18   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f818,plain,
    $false,
    inference(subsumption_resolution,[],[f817,f200]) ).

fof(f200,plain,
    sK15 != sF19,
    inference(definition_folding,[],[f177,f199,f198]) ).

fof(f198,plain,
    cross_product(sK13,sK14) = sF18,
    introduced(function_definition,[]) ).

fof(f199,plain,
    sF19 = intersection(sK15,sF18),
    introduced(function_definition,[]) ).

fof(f177,plain,
    sK15 != intersection(sK15,cross_product(sK13,sK14)),
    inference(cnf_transformation,[],[f112]) ).

fof(f112,plain,
    ( ilf_type(sK13,set_type)
    & sK15 != intersection(sK15,cross_product(sK13,sK14))
    & ilf_type(sK15,relation_type(sK13,sK14))
    & ilf_type(sK14,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15])],[f36,f111,f110,f109]) ).

fof(f109,plain,
    ( ? [X0] :
        ( ilf_type(X0,set_type)
        & ? [X1] :
            ( ? [X2] :
                ( intersection(X2,cross_product(X0,X1)) != X2
                & ilf_type(X2,relation_type(X0,X1)) )
            & ilf_type(X1,set_type) ) )
   => ( ilf_type(sK13,set_type)
      & ? [X1] :
          ( ? [X2] :
              ( intersection(X2,cross_product(sK13,X1)) != X2
              & ilf_type(X2,relation_type(sK13,X1)) )
          & ilf_type(X1,set_type) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f110,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( intersection(X2,cross_product(sK13,X1)) != X2
            & ilf_type(X2,relation_type(sK13,X1)) )
        & ilf_type(X1,set_type) )
   => ( ? [X2] :
          ( intersection(X2,cross_product(sK13,sK14)) != X2
          & ilf_type(X2,relation_type(sK13,sK14)) )
      & ilf_type(sK14,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f111,plain,
    ( ? [X2] :
        ( intersection(X2,cross_product(sK13,sK14)) != X2
        & ilf_type(X2,relation_type(sK13,sK14)) )
   => ( sK15 != intersection(sK15,cross_product(sK13,sK14))
      & ilf_type(sK15,relation_type(sK13,sK14)) ) ),
    introduced(choice_axiom,[]) ).

fof(f36,plain,
    ? [X0] :
      ( ilf_type(X0,set_type)
      & ? [X1] :
          ( ? [X2] :
              ( intersection(X2,cross_product(X0,X1)) != X2
              & ilf_type(X2,relation_type(X0,X1)) )
          & ilf_type(X1,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(f817,plain,
    sK15 = sF19,
    inference(backward_demodulation,[],[f199,f816]) ).

fof(f816,plain,
    sK15 = intersection(sK15,sF18),
    inference(resolution,[],[f814,f261]) ).

fof(f261,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | intersection(X0,X1) = X0 ),
    inference(subsumption_resolution,[],[f260,f168]) ).

fof(f168,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(f260,plain,
    ! [X0,X1] :
      ( intersection(X0,X1) = X0
      | ~ subset(X0,X1)
      | ~ ilf_type(X1,set_type) ),
    inference(subsumption_resolution,[],[f148,f168]) ).

fof(f148,plain,
    ! [X0,X1] :
      ( intersection(X0,X1) = X0
      | ~ ilf_type(X0,set_type)
      | ~ subset(X0,X1)
      | ~ ilf_type(X1,set_type) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( ~ subset(X0,X1)
          | intersection(X0,X1) = X0
          | ~ ilf_type(X1,set_type) ) ),
    inference(flattening,[],[f55]) ).

fof(f55,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(f814,plain,
    subset(sK15,sF18),
    inference(duplicate_literal_removal,[],[f810]) ).

fof(f810,plain,
    ( subset(sK15,sF18)
    | subset(sK15,sF18) ),
    inference(resolution,[],[f757,f233]) ).

fof(f233,plain,
    ! [X0,X1] :
      ( member(sK10(X0,X1),X0)
      | subset(X0,X1) ),
    inference(subsumption_resolution,[],[f232,f168]) ).

fof(f232,plain,
    ! [X0,X1] :
      ( member(sK10(X0,X1),X0)
      | ~ ilf_type(X1,set_type)
      | subset(X0,X1) ),
    inference(subsumption_resolution,[],[f166,f168]) ).

fof(f166,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X0,set_type)
      | member(sK10(X0,X1),X0)
      | ~ ilf_type(X1,set_type)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f104]) ).

fof(f104,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( ( ( subset(X0,X1)
              | ( ilf_type(sK10(X0,X1),set_type)
                & member(sK10(X0,X1),X0)
                & ~ member(sK10(X0,X1),X1) ) )
            & ( ! [X3] :
                  ( ~ ilf_type(X3,set_type)
                  | ~ member(X3,X0)
                  | member(X3,X1) )
              | ~ subset(X0,X1) ) )
          | ~ ilf_type(X1,set_type) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f102,f103]) ).

fof(f103,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ilf_type(X2,set_type)
          & member(X2,X0)
          & ~ member(X2,X1) )
     => ( ilf_type(sK10(X0,X1),set_type)
        & member(sK10(X0,X1),X0)
        & ~ member(sK10(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f102,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( ( ( subset(X0,X1)
              | ? [X2] :
                  ( ilf_type(X2,set_type)
                  & member(X2,X0)
                  & ~ member(X2,X1) ) )
            & ( ! [X3] :
                  ( ~ ilf_type(X3,set_type)
                  | ~ member(X3,X0)
                  | member(X3,X1) )
              | ~ subset(X0,X1) ) )
          | ~ ilf_type(X1,set_type) ) ),
    inference(rectify,[],[f101]) ).

fof(f101,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( ( ( subset(X0,X1)
              | ? [X2] :
                  ( ilf_type(X2,set_type)
                  & member(X2,X0)
                  & ~ member(X2,X1) ) )
            & ( ! [X2] :
                  ( ~ ilf_type(X2,set_type)
                  | ~ member(X2,X0)
                  | member(X2,X1) )
              | ~ subset(X0,X1) ) )
          | ~ ilf_type(X1,set_type) ) ),
    inference(nnf_transformation,[],[f46]) ).

fof(f46,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( ( subset(X0,X1)
          <=> ! [X2] :
                ( ~ ilf_type(X2,set_type)
                | ~ member(X2,X0)
                | member(X2,X1) ) )
          | ~ ilf_type(X1,set_type) ) ),
    inference(flattening,[],[f45]) ).

fof(f45,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(f757,plain,
    ! [X1] :
      ( ~ member(sK10(X1,sF18),sK15)
      | subset(X1,sF18) ),
    inference(resolution,[],[f750,f240]) ).

fof(f240,plain,
    ! [X0,X1] :
      ( ~ member(sK10(X0,X1),X1)
      | subset(X0,X1) ),
    inference(subsumption_resolution,[],[f239,f168]) ).

fof(f239,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ ilf_type(X1,set_type)
      | ~ member(sK10(X0,X1),X1) ),
    inference(subsumption_resolution,[],[f165,f168]) ).

fof(f165,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X0,set_type)
      | subset(X0,X1)
      | ~ ilf_type(X1,set_type)
      | ~ member(sK10(X0,X1),X1) ),
    inference(cnf_transformation,[],[f104]) ).

fof(f750,plain,
    ! [X0] :
      ( member(X0,sF18)
      | ~ member(X0,sK15) ),
    inference(resolution,[],[f748,f267]) ).

fof(f267,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,power_set(X1))
      | ~ member(X2,X0)
      | member(X2,X1) ),
    inference(subsumption_resolution,[],[f266,f168]) ).

fof(f266,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,power_set(X1))
      | ~ member(X2,X0)
      | ~ ilf_type(X2,set_type)
      | member(X2,X1) ),
    inference(subsumption_resolution,[],[f265,f168]) ).

fof(f265,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,X0)
      | ~ ilf_type(X0,set_type)
      | ~ member(X0,power_set(X1))
      | member(X2,X1)
      | ~ ilf_type(X2,set_type) ),
    inference(subsumption_resolution,[],[f130,f168]) ).

fof(f130,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,power_set(X1))
      | ~ ilf_type(X1,set_type)
      | member(X2,X1)
      | ~ member(X2,X0)
      | ~ ilf_type(X2,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f77,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ilf_type(X1,set_type)
          | ( ( ! [X2] :
                  ( member(X2,X1)
                  | ~ member(X2,X0)
                  | ~ ilf_type(X2,set_type) )
              | ~ member(X0,power_set(X1)) )
            & ( member(X0,power_set(X1))
              | ( ~ member(sK2(X0,X1),X1)
                & member(sK2(X0,X1),X0)
                & ilf_type(sK2(X0,X1),set_type) ) ) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f75,f76]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ~ member(X3,X1)
          & member(X3,X0)
          & ilf_type(X3,set_type) )
     => ( ~ member(sK2(X0,X1),X1)
        & member(sK2(X0,X1),X0)
        & ilf_type(sK2(X0,X1),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f75,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ilf_type(X1,set_type)
          | ( ( ! [X2] :
                  ( member(X2,X1)
                  | ~ member(X2,X0)
                  | ~ ilf_type(X2,set_type) )
              | ~ member(X0,power_set(X1)) )
            & ( member(X0,power_set(X1))
              | ? [X3] :
                  ( ~ member(X3,X1)
                  & member(X3,X0)
                  & ilf_type(X3,set_type) ) ) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(rectify,[],[f74]) ).

fof(f74,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ilf_type(X1,set_type)
          | ( ( ! [X2] :
                  ( member(X2,X1)
                  | ~ member(X2,X0)
                  | ~ ilf_type(X2,set_type) )
              | ~ member(X0,power_set(X1)) )
            & ( member(X0,power_set(X1))
              | ? [X2] :
                  ( ~ member(X2,X1)
                  & member(X2,X0)
                  & ilf_type(X2,set_type) ) ) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ilf_type(X1,set_type)
          | ( ! [X2] :
                ( member(X2,X1)
                | ~ member(X2,X0)
                | ~ ilf_type(X2,set_type) )
          <=> member(X0,power_set(X1)) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f48]) ).

fof(f48,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ! [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(ennf_transformation,[],[f19]) ).

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

fof(f748,plain,
    member(sK15,power_set(sF18)),
    inference(resolution,[],[f721,f202]) ).

fof(f202,plain,
    ilf_type(sK15,sF20),
    inference(definition_folding,[],[f176,f201]) ).

fof(f201,plain,
    sF20 = relation_type(sK13,sK14),
    introduced(function_definition,[]) ).

fof(f176,plain,
    ilf_type(sK15,relation_type(sK13,sK14)),
    inference(cnf_transformation,[],[f112]) ).

fof(f721,plain,
    ! [X3] :
      ( ~ ilf_type(X3,sF20)
      | member(X3,power_set(sF18)) ),
    inference(resolution,[],[f583,f610]) ).

fof(f610,plain,
    ! [X0] :
      ( ilf_type(X0,subset_type(sF18))
      | ~ ilf_type(X0,sF20) ),
    inference(forward_demodulation,[],[f609,f201]) ).

fof(f609,plain,
    ! [X0] :
      ( ilf_type(X0,subset_type(sF18))
      | ~ ilf_type(X0,relation_type(sK13,sK14)) ),
    inference(subsumption_resolution,[],[f608,f168]) ).

fof(f608,plain,
    ! [X0] :
      ( ~ ilf_type(X0,relation_type(sK13,sK14))
      | ~ ilf_type(sK13,set_type)
      | ilf_type(X0,subset_type(sF18)) ),
    inference(subsumption_resolution,[],[f605,f175]) ).

fof(f175,plain,
    ilf_type(sK14,set_type),
    inference(cnf_transformation,[],[f112]) ).

fof(f605,plain,
    ! [X0] :
      ( ~ ilf_type(X0,relation_type(sK13,sK14))
      | ilf_type(X0,subset_type(sF18))
      | ~ ilf_type(sK14,set_type)
      | ~ ilf_type(sK13,set_type) ),
    inference(superposition,[],[f182,f198]) ).

fof(f182,plain,
    ! [X2,X0,X1] :
      ( ilf_type(X2,subset_type(cross_product(X0,X1)))
      | ~ ilf_type(X0,set_type)
      | ~ ilf_type(X2,relation_type(X0,X1))
      | ~ ilf_type(X1,set_type) ),
    inference(cnf_transformation,[],[f113]) ).

fof(f113,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,[],[f59]) ).

fof(f59,plain,
    ! [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)) ) ) ) ),
    inference(ennf_transformation,[],[f6]) ).

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

fof(f583,plain,
    ! [X2,X3] :
      ( ~ ilf_type(X2,subset_type(X3))
      | member(X2,power_set(X3)) ),
    inference(subsumption_resolution,[],[f582,f168]) ).

fof(f582,plain,
    ! [X2,X3] :
      ( ~ ilf_type(X3,set_type)
      | member(X2,power_set(X3))
      | ~ ilf_type(X2,subset_type(X3)) ),
    inference(subsumption_resolution,[],[f581,f238]) ).

fof(f238,plain,
    ! [X0] : ~ empty(power_set(X0)),
    inference(subsumption_resolution,[],[f170,f168]) ).

fof(f170,plain,
    ! [X0] :
      ( ~ empty(power_set(X0))
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f57]) ).

fof(f57,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ( ilf_type(power_set(X0),set_type)
        & ~ empty(power_set(X0)) ) ),
    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(f581,plain,
    ! [X2,X3] :
      ( empty(power_set(X3))
      | ~ ilf_type(X3,set_type)
      | member(X2,power_set(X3))
      | ~ ilf_type(X2,subset_type(X3)) ),
    inference(subsumption_resolution,[],[f580,f168]) ).

fof(f580,plain,
    ! [X2,X3] :
      ( ~ ilf_type(X2,set_type)
      | member(X2,power_set(X3))
      | ~ ilf_type(X3,set_type)
      | empty(power_set(X3))
      | ~ ilf_type(X2,subset_type(X3)) ),
    inference(resolution,[],[f162,f231]) ).

fof(f231,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X0,member_type(X1))
      | empty(X1)
      | member(X0,X1) ),
    inference(subsumption_resolution,[],[f230,f168]) ).

fof(f230,plain,
    ! [X0,X1] :
      ( empty(X1)
      | member(X0,X1)
      | ~ ilf_type(X0,member_type(X1))
      | ~ ilf_type(X1,set_type) ),
    inference(subsumption_resolution,[],[f138,f168]) ).

fof(f138,plain,
    ! [X0,X1] :
      ( empty(X1)
      | ~ ilf_type(X0,member_type(X1))
      | ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type)
      | member(X0,X1) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f84,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [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) ) ),
    inference(nnf_transformation,[],[f41]) ).

fof(f41,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( ( ilf_type(X0,member_type(X1))
          <=> member(X0,X1) )
          | ~ ilf_type(X1,set_type)
          | empty(X1) ) ),
    inference(flattening,[],[f40]) ).

fof(f40,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ilf_type(X0,member_type(X1))
          <=> member(X0,X1) )
          | empty(X1)
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f21]) ).

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

fof(f162,plain,
    ! [X0,X1] :
      ( ilf_type(X1,member_type(power_set(X0)))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,subset_type(X0)) ),
    inference(cnf_transformation,[],[f100]) ).

fof(f100,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,[],[f66]) ).

fof(f66,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) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SET656+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n016.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
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 30 14:33:01 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.20/0.50  % (23847)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.20/0.50  % (23839)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.20/0.50  % (23830)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.51  % (23836)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.20/0.51  % (23830)Instruction limit reached!
% 0.20/0.51  % (23830)------------------------------
% 0.20/0.51  % (23830)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (23830)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51  % (23830)Termination reason: Unknown
% 0.20/0.51  % (23830)Termination phase: Saturation
% 0.20/0.51  
% 0.20/0.51  % (23830)Memory used [KB]: 5500
% 0.20/0.51  % (23830)Time elapsed: 0.070 s
% 0.20/0.51  % (23830)Instructions burned: 8 (million)
% 0.20/0.51  % (23830)------------------------------
% 0.20/0.51  % (23830)------------------------------
% 0.20/0.51  % (23827)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.52  % (23834)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.52  % (23825)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.20/0.52  % (23829)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.52  % (23835)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.52  % (23823)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.20/0.53  % (23848)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.20/0.53  % (23837)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.53  % (23842)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.53  % (23851)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.20/0.53  % (23832)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.53  % (23838)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.53  % (23832)Instruction limit reached!
% 0.20/0.53  % (23832)------------------------------
% 0.20/0.53  % (23832)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (23832)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (23832)Termination reason: Unknown
% 0.20/0.53  % (23832)Termination phase: Preprocessing 3
% 0.20/0.53  
% 0.20/0.53  % (23832)Memory used [KB]: 895
% 0.20/0.53  % (23832)Time elapsed: 0.002 s
% 0.20/0.53  % (23832)Instructions burned: 3 (million)
% 0.20/0.53  % (23832)------------------------------
% 0.20/0.53  % (23832)------------------------------
% 0.20/0.54  % (23826)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.54  % (23840)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.54  % (23849)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.20/0.54  % (23846)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 1.49/0.54  % (23839)First to succeed.
% 1.49/0.54  % (23828)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 1.49/0.54  % (23852)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 1.49/0.55  % (23844)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 1.49/0.55  % (23841)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 1.49/0.55  TRYING [1]
% 1.49/0.55  % (23824)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.49/0.55  TRYING [2]
% 1.49/0.55  % (23845)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 1.49/0.55  TRYING [1]
% 1.49/0.55  % (23839)Refutation found. Thanks to Tanya!
% 1.49/0.55  % SZS status Theorem for theBenchmark
% 1.49/0.55  % SZS output start Proof for theBenchmark
% See solution above
% 1.49/0.55  % (23839)------------------------------
% 1.49/0.55  % (23839)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.49/0.55  % (23839)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.49/0.55  % (23839)Termination reason: Refutation
% 1.49/0.55  
% 1.49/0.55  % (23839)Memory used [KB]: 1663
% 1.49/0.55  % (23839)Time elapsed: 0.094 s
% 1.49/0.55  % (23839)Instructions burned: 32 (million)
% 1.49/0.55  % (23839)------------------------------
% 1.49/0.55  % (23839)------------------------------
% 1.49/0.55  % (23819)Success in time 0.2 s
%------------------------------------------------------------------------------