TSTP Solution File: SET669+3 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET669+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 : n012.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 18:25:17 EDT 2022

% Result   : Theorem 1.81s 0.62s
% Output   : Refutation 1.81s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   19
% Syntax   : Number of formulae    :  110 (  21 unt;   0 def)
%            Number of atoms       :  455 (  27 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  573 ( 228   ~; 224   |;  72   &)
%                                         (  13 <=>;  36  =>;   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    :   17 (  17 usr;   8 con; 0-3 aty)
%            Number of variables   :  187 ( 166   !;  21   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f669,plain,
    $false,
    inference(subsumption_resolution,[],[f665,f146]) ).

fof(f146,plain,
    ilf_type(sK4,set_type),
    inference(cnf_transformation,[],[f95]) ).

fof(f95,plain,
    ( ilf_type(sK3,set_type)
    & ( range(sK3,sK4,sK5) != sK4
      | ~ subset(sK4,domain(sK3,sK4,sK5)) )
    & subset(identity_relation_of(sK4),sK5)
    & ilf_type(sK5,relation_type(sK3,sK4))
    & ilf_type(sK4,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f50,f94,f93,f92]) ).

fof(f92,plain,
    ( ? [X0] :
        ( ilf_type(X0,set_type)
        & ? [X1] :
            ( ? [X2] :
                ( ( range(X0,X1,X2) != X1
                  | ~ subset(X1,domain(X0,X1,X2)) )
                & subset(identity_relation_of(X1),X2)
                & ilf_type(X2,relation_type(X0,X1)) )
            & ilf_type(X1,set_type) ) )
   => ( ilf_type(sK3,set_type)
      & ? [X1] :
          ( ? [X2] :
              ( ( range(sK3,X1,X2) != X1
                | ~ subset(X1,domain(sK3,X1,X2)) )
              & subset(identity_relation_of(X1),X2)
              & ilf_type(X2,relation_type(sK3,X1)) )
          & ilf_type(X1,set_type) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f93,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ( range(sK3,X1,X2) != X1
              | ~ subset(X1,domain(sK3,X1,X2)) )
            & subset(identity_relation_of(X1),X2)
            & ilf_type(X2,relation_type(sK3,X1)) )
        & ilf_type(X1,set_type) )
   => ( ? [X2] :
          ( ( range(sK3,sK4,X2) != sK4
            | ~ subset(sK4,domain(sK3,sK4,X2)) )
          & subset(identity_relation_of(sK4),X2)
          & ilf_type(X2,relation_type(sK3,sK4)) )
      & ilf_type(sK4,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f94,plain,
    ( ? [X2] :
        ( ( range(sK3,sK4,X2) != sK4
          | ~ subset(sK4,domain(sK3,sK4,X2)) )
        & subset(identity_relation_of(sK4),X2)
        & ilf_type(X2,relation_type(sK3,sK4)) )
   => ( ( range(sK3,sK4,sK5) != sK4
        | ~ subset(sK4,domain(sK3,sK4,sK5)) )
      & subset(identity_relation_of(sK4),sK5)
      & ilf_type(sK5,relation_type(sK3,sK4)) ) ),
    introduced(choice_axiom,[]) ).

fof(f50,plain,
    ? [X0] :
      ( ilf_type(X0,set_type)
      & ? [X1] :
          ( ? [X2] :
              ( ( range(X0,X1,X2) != X1
                | ~ subset(X1,domain(X0,X1,X2)) )
              & subset(identity_relation_of(X1),X2)
              & ilf_type(X2,relation_type(X0,X1)) )
          & ilf_type(X1,set_type) ) ),
    inference(flattening,[],[f49]) ).

fof(f49,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ( range(X0,X1,X2) != X1
                | ~ subset(X1,domain(X0,X1,X2)) )
              & subset(identity_relation_of(X1),X2)
              & ilf_type(X2,relation_type(X0,X1)) )
          & ilf_type(X1,set_type) )
      & ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f34,negated_conjecture,
    ~ ! [X0] :
        ( ilf_type(X0,set_type)
       => ! [X1] :
            ( ilf_type(X1,set_type)
           => ! [X2] :
                ( ilf_type(X2,relation_type(X0,X1))
               => ( subset(identity_relation_of(X1),X2)
                 => ( subset(X1,domain(X0,X1,X2))
                    & range(X0,X1,X2) = X1 ) ) ) ) ),
    inference(negated_conjecture,[],[f33]) ).

fof(f33,conjecture,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,relation_type(X0,X1))
             => ( subset(identity_relation_of(X1),X2)
               => ( subset(X1,domain(X0,X1,X2))
                  & range(X0,X1,X2) = X1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_32) ).

fof(f665,plain,
    ~ ilf_type(sK4,set_type),
    inference(resolution,[],[f647,f157]) ).

fof(f157,plain,
    ! [X0] :
      ( ~ empty(power_set(X0))
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,plain,
    ! [X0] :
      ( ( ~ empty(power_set(X0))
        & ilf_type(power_set(X0),set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f21]) ).

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

fof(f647,plain,
    empty(power_set(sK4)),
    inference(subsumption_resolution,[],[f645,f531]) ).

fof(f531,plain,
    ~ subset(sF15,sK4),
    inference(subsumption_resolution,[],[f530,f146]) ).

fof(f530,plain,
    ( ~ subset(sF15,sK4)
    | ~ ilf_type(sK4,set_type) ),
    inference(subsumption_resolution,[],[f529,f318]) ).

fof(f318,plain,
    sF15 != sK4,
    inference(resolution,[],[f309,f191]) ).

fof(f191,plain,
    ( ~ subset(sK4,sF16)
    | sF15 != sK4 ),
    inference(definition_folding,[],[f149,f190,f189]) ).

fof(f189,plain,
    sF15 = range(sK3,sK4,sK5),
    introduced(function_definition,[]) ).

fof(f190,plain,
    sF16 = domain(sK3,sK4,sK5),
    introduced(function_definition,[]) ).

fof(f149,plain,
    ( range(sK3,sK4,sK5) != sK4
    | ~ subset(sK4,domain(sK3,sK4,sK5)) ),
    inference(cnf_transformation,[],[f95]) ).

fof(f309,plain,
    subset(sK4,sF16),
    inference(subsumption_resolution,[],[f308,f193]) ).

fof(f193,plain,
    subset(sF17,sK5),
    inference(definition_folding,[],[f148,f192]) ).

fof(f192,plain,
    sF17 = identity_relation_of(sK4),
    introduced(function_definition,[]) ).

fof(f148,plain,
    subset(identity_relation_of(sK4),sK5),
    inference(cnf_transformation,[],[f95]) ).

fof(f308,plain,
    ( ~ subset(sF17,sK5)
    | subset(sK4,sF16) ),
    inference(superposition,[],[f305,f192]) ).

fof(f305,plain,
    ! [X0] :
      ( ~ subset(identity_relation_of(X0),sK5)
      | subset(X0,sF16) ),
    inference(subsumption_resolution,[],[f304,f195]) ).

fof(f195,plain,
    ilf_type(sK5,sF18),
    inference(definition_folding,[],[f147,f194]) ).

fof(f194,plain,
    relation_type(sK3,sK4) = sF18,
    introduced(function_definition,[]) ).

fof(f147,plain,
    ilf_type(sK5,relation_type(sK3,sK4)),
    inference(cnf_transformation,[],[f95]) ).

fof(f304,plain,
    ! [X0] :
      ( ~ ilf_type(sK5,sF18)
      | ~ subset(identity_relation_of(X0),sK5)
      | subset(X0,sF16) ),
    inference(forward_demodulation,[],[f303,f194]) ).

fof(f303,plain,
    ! [X0] :
      ( ~ ilf_type(sK5,relation_type(sK3,sK4))
      | subset(X0,sF16)
      | ~ subset(identity_relation_of(X0),sK5) ),
    inference(superposition,[],[f208,f190]) ).

fof(f208,plain,
    ! [X2,X3,X0,X1] :
      ( subset(X2,domain(X0,X1,X3))
      | ~ ilf_type(X3,relation_type(X0,X1))
      | ~ subset(identity_relation_of(X2),X3) ),
    inference(subsumption_resolution,[],[f207,f175]) ).

fof(f175,plain,
    ! [X0] : ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f32]) ).

fof(f32,axiom,
    ! [X0] : ilf_type(X0,set_type),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p32) ).

fof(f207,plain,
    ! [X2,X3,X0,X1] :
      ( ~ ilf_type(X3,relation_type(X0,X1))
      | ~ ilf_type(X0,set_type)
      | ~ subset(identity_relation_of(X2),X3)
      | subset(X2,domain(X0,X1,X3)) ),
    inference(subsumption_resolution,[],[f206,f175]) ).

fof(f206,plain,
    ! [X2,X3,X0,X1] :
      ( subset(X2,domain(X0,X1,X3))
      | ~ ilf_type(X2,set_type)
      | ~ ilf_type(X0,set_type)
      | ~ ilf_type(X3,relation_type(X0,X1))
      | ~ subset(identity_relation_of(X2),X3) ),
    inference(subsumption_resolution,[],[f182,f175]) ).

fof(f182,plain,
    ! [X2,X3,X0,X1] :
      ( subset(X2,domain(X0,X1,X3))
      | ~ subset(identity_relation_of(X2),X3)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X3,relation_type(X0,X1))
      | ~ ilf_type(X2,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( ! [X2] :
              ( ~ ilf_type(X2,set_type)
              | ! [X3] :
                  ( ~ subset(identity_relation_of(X2),X3)
                  | ( subset(X2,domain(X0,X1,X3))
                    & subset(X2,range(X0,X1,X3)) )
                  | ~ ilf_type(X3,relation_type(X0,X1)) ) )
          | ~ ilf_type(X1,set_type) ) ),
    inference(flattening,[],[f71]) ).

fof(f71,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ( subset(X2,domain(X0,X1,X3))
                    & subset(X2,range(X0,X1,X3)) )
                  | ~ subset(identity_relation_of(X2),X3)
                  | ~ ilf_type(X3,relation_type(X0,X1)) )
              | ~ ilf_type(X2,set_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,set_type)
             => ! [X3] :
                  ( ilf_type(X3,relation_type(X0,X1))
                 => ( subset(identity_relation_of(X2),X3)
                   => ( subset(X2,domain(X0,X1,X3))
                      & subset(X2,range(X0,X1,X3)) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).

fof(f529,plain,
    ( sF15 = sK4
    | ~ ilf_type(sK4,set_type)
    | ~ subset(sF15,sK4) ),
    inference(subsumption_resolution,[],[f528,f175]) ).

fof(f528,plain,
    ( ~ subset(sF15,sK4)
    | ~ ilf_type(sF15,set_type)
    | ~ ilf_type(sK4,set_type)
    | sF15 = sK4 ),
    inference(resolution,[],[f510,f137]) ).

fof(f137,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | X0 = X1
      | ~ subset(X0,X1)
      | ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type) ),
    inference(cnf_transformation,[],[f87]) ).

fof(f87,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( ( subset(X1,X0)
                & subset(X0,X1) )
              | X0 != X1 )
            & ( X0 = X1
              | ~ subset(X1,X0)
              | ~ subset(X0,X1) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f86]) ).

fof(f86,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( ( subset(X1,X0)
                & subset(X0,X1) )
              | X0 != X1 )
            & ( X0 = X1
              | ~ subset(X1,X0)
              | ~ subset(X0,X1) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f65]) ).

fof(f65,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( subset(X1,X0)
              & subset(X0,X1) )
          <=> X0 = X1 )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( ( subset(X1,X0)
              & subset(X0,X1) )
          <=> X0 = X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9) ).

fof(f510,plain,
    subset(sK4,sF15),
    inference(subsumption_resolution,[],[f509,f193]) ).

fof(f509,plain,
    ( ~ subset(sF17,sK5)
    | subset(sK4,sF15) ),
    inference(superposition,[],[f499,f192]) ).

fof(f499,plain,
    ! [X0] :
      ( ~ subset(identity_relation_of(X0),sK5)
      | subset(X0,sF15) ),
    inference(forward_demodulation,[],[f495,f189]) ).

fof(f495,plain,
    ! [X0] :
      ( subset(X0,range(sK3,sK4,sK5))
      | ~ subset(identity_relation_of(X0),sK5) ),
    inference(resolution,[],[f460,f195]) ).

fof(f460,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X0,sF18)
      | subset(X1,range(sK3,sK4,X0))
      | ~ subset(identity_relation_of(X1),X0) ),
    inference(subsumption_resolution,[],[f459,f150]) ).

fof(f150,plain,
    ilf_type(sK3,set_type),
    inference(cnf_transformation,[],[f95]) ).

fof(f459,plain,
    ! [X0,X1] :
      ( ~ subset(identity_relation_of(X1),X0)
      | ~ ilf_type(X0,sF18)
      | ~ ilf_type(sK3,set_type)
      | subset(X1,range(sK3,sK4,X0)) ),
    inference(subsumption_resolution,[],[f458,f175]) ).

fof(f458,plain,
    ! [X0,X1] :
      ( ~ subset(identity_relation_of(X1),X0)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(sK3,set_type)
      | subset(X1,range(sK3,sK4,X0))
      | ~ ilf_type(X0,sF18) ),
    inference(subsumption_resolution,[],[f456,f146]) ).

fof(f456,plain,
    ! [X0,X1] :
      ( ~ ilf_type(sK4,set_type)
      | ~ ilf_type(sK3,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,sF18)
      | ~ subset(identity_relation_of(X1),X0)
      | subset(X1,range(sK3,sK4,X0)) ),
    inference(superposition,[],[f181,f194]) ).

fof(f181,plain,
    ! [X2,X3,X0,X1] :
      ( ~ ilf_type(X3,relation_type(X0,X1))
      | ~ ilf_type(X0,set_type)
      | ~ ilf_type(X2,set_type)
      | ~ subset(identity_relation_of(X2),X3)
      | ~ ilf_type(X1,set_type)
      | subset(X2,range(X0,X1,X3)) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f645,plain,
    ( subset(sF15,sK4)
    | empty(power_set(sK4)) ),
    inference(duplicate_literal_removal,[],[f643]) ).

fof(f643,plain,
    ( subset(sF15,sK4)
    | subset(sF15,sK4)
    | empty(power_set(sK4)) ),
    inference(resolution,[],[f555,f210]) ).

fof(f210,plain,
    ! [X0,X1] :
      ( ~ member(sK2(X0,X1),X1)
      | subset(X0,X1) ),
    inference(subsumption_resolution,[],[f209,f175]) ).

fof(f209,plain,
    ! [X0,X1] :
      ( ~ member(sK2(X0,X1),X1)
      | subset(X0,X1)
      | ~ ilf_type(X1,set_type) ),
    inference(subsumption_resolution,[],[f142,f175]) ).

fof(f142,plain,
    ! [X0,X1] :
      ( ~ member(sK2(X0,X1),X1)
      | ~ ilf_type(X0,set_type)
      | subset(X0,X1)
      | ~ ilf_type(X1,set_type) ),
    inference(cnf_transformation,[],[f91]) ).

fof(f91,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( ! [X2] :
                  ( ~ member(X2,X0)
                  | member(X2,X1)
                  | ~ ilf_type(X2,set_type) )
              | ~ subset(X0,X1) )
            & ( subset(X0,X1)
              | ( member(sK2(X0,X1),X0)
                & ~ member(sK2(X0,X1),X1)
                & ilf_type(sK2(X0,X1),set_type) ) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f89,f90]) ).

fof(f90,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( member(X3,X0)
          & ~ member(X3,X1)
          & ilf_type(X3,set_type) )
     => ( member(sK2(X0,X1),X0)
        & ~ member(sK2(X0,X1),X1)
        & ilf_type(sK2(X0,X1),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f89,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( ! [X2] :
                  ( ~ member(X2,X0)
                  | member(X2,X1)
                  | ~ ilf_type(X2,set_type) )
              | ~ subset(X0,X1) )
            & ( subset(X0,X1)
              | ? [X3] :
                  ( member(X3,X0)
                  & ~ member(X3,X1)
                  & ilf_type(X3,set_type) ) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(rectify,[],[f88]) ).

fof(f88,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( ! [X2] :
                  ( ~ member(X2,X0)
                  | member(X2,X1)
                  | ~ ilf_type(X2,set_type) )
              | ~ subset(X0,X1) )
            & ( subset(X0,X1)
              | ? [X2] :
                  ( member(X2,X0)
                  & ~ member(X2,X1)
                  & ilf_type(X2,set_type) ) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f56]) ).

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

fof(f55,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,[],[f7]) ).

fof(f7,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',p7) ).

fof(f555,plain,
    ! [X1] :
      ( member(sK2(sF15,X1),sK4)
      | empty(power_set(sK4))
      | subset(sF15,X1) ),
    inference(resolution,[],[f487,f214]) ).

fof(f214,plain,
    ! [X0,X1] :
      ( member(sK2(X0,X1),X0)
      | subset(X0,X1) ),
    inference(subsumption_resolution,[],[f213,f175]) ).

fof(f213,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ ilf_type(X0,set_type)
      | member(sK2(X0,X1),X0) ),
    inference(subsumption_resolution,[],[f143,f175]) ).

fof(f143,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ ilf_type(X1,set_type)
      | member(sK2(X0,X1),X0)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f91]) ).

fof(f487,plain,
    ! [X0] :
      ( ~ member(X0,sF15)
      | empty(power_set(sK4))
      | member(X0,sK4) ),
    inference(subsumption_resolution,[],[f486,f175]) ).

fof(f486,plain,
    ! [X0] :
      ( empty(power_set(sK4))
      | ~ member(X0,sF15)
      | ~ ilf_type(X0,set_type)
      | member(X0,sK4) ),
    inference(subsumption_resolution,[],[f485,f146]) ).

fof(f485,plain,
    ! [X0] :
      ( member(X0,sK4)
      | ~ ilf_type(sK4,set_type)
      | ~ ilf_type(X0,set_type)
      | ~ member(X0,sF15)
      | empty(power_set(sK4)) ),
    inference(subsumption_resolution,[],[f483,f175]) ).

fof(f483,plain,
    ! [X0] :
      ( ~ ilf_type(sF15,set_type)
      | ~ member(X0,sF15)
      | empty(power_set(sK4))
      | ~ ilf_type(X0,set_type)
      | ~ ilf_type(sK4,set_type)
      | member(X0,sK4) ),
    inference(resolution,[],[f478,f170]) ).

fof(f170,plain,
    ! [X3,X0,X1] :
      ( ~ member(X0,power_set(X1))
      | ~ ilf_type(X3,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type)
      | ~ member(X3,X0)
      | member(X3,X1) ),
    inference(cnf_transformation,[],[f113]) ).

fof(f113,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( ( ( member(X0,power_set(X1))
              | ( ~ member(sK12(X0,X1),X1)
                & member(sK12(X0,X1),X0)
                & ilf_type(sK12(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) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f111,f112]) ).

fof(f112,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0)
          & ilf_type(X2,set_type) )
     => ( ~ member(sK12(X0,X1),X1)
        & member(sK12(X0,X1),X0)
        & ilf_type(sK12(X0,X1),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f111,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [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) ) ),
    inference(rectify,[],[f110]) ).

fof(f110,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [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) ) ),
    inference(nnf_transformation,[],[f54]) ).

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

fof(f53,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,[],[f20]) ).

fof(f20,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',p20) ).

fof(f478,plain,
    ( member(sF15,power_set(sK4))
    | empty(power_set(sK4)) ),
    inference(resolution,[],[f474,f268]) ).

fof(f268,plain,
    ! [X2,X1] :
      ( ~ ilf_type(X1,subset_type(X2))
      | member(X1,power_set(X2))
      | empty(power_set(X2)) ),
    inference(subsumption_resolution,[],[f267,f175]) ).

fof(f267,plain,
    ! [X2,X1] :
      ( ~ ilf_type(X1,set_type)
      | member(X1,power_set(X2))
      | ~ ilf_type(X1,subset_type(X2))
      | empty(power_set(X2)) ),
    inference(subsumption_resolution,[],[f263,f175]) ).

fof(f263,plain,
    ! [X2,X1] :
      ( empty(power_set(X2))
      | ~ ilf_type(power_set(X2),set_type)
      | ~ ilf_type(X1,set_type)
      | member(X1,power_set(X2))
      | ~ ilf_type(X1,subset_type(X2)) ),
    inference(resolution,[],[f121,f222]) ).

fof(f222,plain,
    ! [X0,X1] :
      ( ilf_type(X1,member_type(power_set(X0)))
      | ~ ilf_type(X1,subset_type(X0)) ),
    inference(subsumption_resolution,[],[f221,f175]) ).

fof(f221,plain,
    ! [X0,X1] :
      ( ilf_type(X1,member_type(power_set(X0)))
      | ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,subset_type(X0)) ),
    inference(subsumption_resolution,[],[f165,f175]) ).

fof(f165,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X1,subset_type(X0))
      | ~ ilf_type(X1,set_type)
      | ilf_type(X1,member_type(power_set(X0)))
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f107]) ).

fof(f107,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ilf_type(X1,set_type)
          | ( ( 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(X0,set_type) ),
    inference(nnf_transformation,[],[f60]) ).

fof(f60,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ilf_type(X1,set_type)
          | ( ilf_type(X1,subset_type(X0))
          <=> ilf_type(X1,member_type(power_set(X0))) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,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',p16) ).

fof(f121,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X0,member_type(X1))
      | ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type)
      | empty(X1)
      | member(X0,X1) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f77,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( empty(X1)
          | ( ( ilf_type(X0,member_type(X1))
              | ~ member(X0,X1) )
            & ( member(X0,X1)
              | ~ ilf_type(X0,member_type(X1)) ) )
          | ~ ilf_type(X1,set_type) ) ),
    inference(nnf_transformation,[],[f39]) ).

fof(f39,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( empty(X1)
          | ( ilf_type(X0,member_type(X1))
          <=> member(X0,X1) )
          | ~ ilf_type(X1,set_type) ) ),
    inference(flattening,[],[f38]) ).

fof(f38,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,[],[f22]) ).

fof(f22,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',p22) ).

fof(f474,plain,
    ilf_type(sF15,subset_type(sK4)),
    inference(forward_demodulation,[],[f469,f189]) ).

fof(f469,plain,
    ilf_type(range(sK3,sK4,sK5),subset_type(sK4)),
    inference(resolution,[],[f349,f195]) ).

fof(f349,plain,
    ! [X0] :
      ( ~ ilf_type(X0,sF18)
      | ilf_type(range(sK3,sK4,X0),subset_type(sK4)) ),
    inference(subsumption_resolution,[],[f348,f150]) ).

fof(f348,plain,
    ! [X0] :
      ( ~ ilf_type(X0,sF18)
      | ilf_type(range(sK3,sK4,X0),subset_type(sK4))
      | ~ ilf_type(sK3,set_type) ),
    inference(subsumption_resolution,[],[f346,f146]) ).

fof(f346,plain,
    ! [X0] :
      ( ~ ilf_type(X0,sF18)
      | ilf_type(range(sK3,sK4,X0),subset_type(sK4))
      | ~ ilf_type(sK4,set_type)
      | ~ ilf_type(sK3,set_type) ),
    inference(superposition,[],[f136,f194]) ).

fof(f136,plain,
    ! [X2,X0,X1] :
      ( ~ ilf_type(X2,relation_type(X0,X1))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type)
      | ilf_type(range(X0,X1,X2),subset_type(X1)) ),
    inference(cnf_transformation,[],[f57]) ).

fof(f57,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( ! [X2] :
              ( ilf_type(range(X0,X1,X2),subset_type(X1))
              | ~ ilf_type(X2,relation_type(X0,X1)) )
          | ~ ilf_type(X1,set_type) ) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f31,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,relation_type(X0,X1))
             => ilf_type(range(X0,X1,X2),subset_type(X1)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p31) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SET669+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13  % 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 : n012.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 14:12:20 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.55  % (6979)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)
% 0.19/0.55  TRYING [1]
% 0.19/0.56  % (6996)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)
% 0.19/0.56  % (6988)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)
% 0.19/0.56  % (6995)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)
% 0.19/0.57  % (6980)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.57  TRYING [2]
% 0.19/0.58  % (6980)Instruction limit reached!
% 0.19/0.58  % (6980)------------------------------
% 0.19/0.58  % (6980)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.58  % (6980)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.58  % (6980)Termination reason: Unknown
% 0.19/0.58  % (6980)Termination phase: Saturation
% 0.19/0.58  
% 0.19/0.58  % (6980)Memory used [KB]: 5500
% 0.19/0.58  % (6980)Time elapsed: 0.088 s
% 0.19/0.58  % (6980)Instructions burned: 7 (million)
% 0.19/0.58  % (6980)------------------------------
% 0.19/0.58  % (6980)------------------------------
% 0.19/0.59  TRYING [3]
% 0.19/0.59  % (6987)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)
% 0.19/0.59  % (6981)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.59  % (6978)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)
% 0.19/0.59  % (6981)Instruction limit reached!
% 0.19/0.59  % (6981)------------------------------
% 0.19/0.59  % (6981)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.59  % (6981)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.59  % (6981)Termination reason: Unknown
% 0.19/0.59  % (6981)Termination phase: Preprocessing 1
% 0.19/0.59  
% 0.19/0.59  % (6981)Memory used [KB]: 895
% 0.19/0.59  % (6981)Time elapsed: 0.002 s
% 0.19/0.59  % (6981)Instructions burned: 2 (million)
% 0.19/0.59  % (6981)------------------------------
% 0.19/0.59  % (6981)------------------------------
% 0.19/0.59  % (6974)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)
% 0.19/0.60  % (6976)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)
% 0.19/0.60  % (6977)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.81/0.61  % (6988)First to succeed.
% 1.81/0.61  % (6973)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)
% 1.81/0.61  % (6975)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)
% 1.81/0.61  % (6998)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 1.81/0.61  % (7000)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)
% 1.81/0.61  % (7002)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 1.81/0.62  % (6979)Instruction limit reached!
% 1.81/0.62  % (6979)------------------------------
% 1.81/0.62  % (6979)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.81/0.62  % (6990)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 1.81/0.62  % (7001)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 1.81/0.62  % (6988)Refutation found. Thanks to Tanya!
% 1.81/0.62  % SZS status Theorem for theBenchmark
% 1.81/0.62  % SZS output start Proof for theBenchmark
% See solution above
% 1.81/0.62  % (6988)------------------------------
% 1.81/0.62  % (6988)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.81/0.62  % (6988)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.81/0.62  % (6988)Termination reason: Refutation
% 1.81/0.62  
% 1.81/0.62  % (6988)Memory used [KB]: 1407
% 1.81/0.62  % (6988)Time elapsed: 0.114 s
% 1.81/0.62  % (6988)Instructions burned: 25 (million)
% 1.81/0.62  % (6988)------------------------------
% 1.81/0.62  % (6988)------------------------------
% 1.81/0.62  % (6972)Success in time 0.267 s
%------------------------------------------------------------------------------