TSTP Solution File: SET654+3 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET654+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_uns --cores 0 -t %d %s

% Computer : n009.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 18:21:45 EDT 2022

% Result   : Theorem 0.18s 0.50s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   29 (   9 unt;   0 def)
%            Number of atoms       :  137 (   0 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  158 (  50   ~;  36   |;  46   &)
%                                         (   0 <=>;  26  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   71 (  47   !;  24   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f163,plain,
    $false,
    inference(subsumption_resolution,[],[f158,f147]) ).

fof(f147,plain,
    ~ subset(range_of(sK9),sK7),
    inference(unit_resulting_resolution,[],[f90,f90,f90,f111,f113,f88]) ).

fof(f88,plain,
    ! [X2,X3,X0,X1] :
      ( ~ ilf_type(X1,set_type)
      | ~ ilf_type(X2,set_type)
      | ~ ilf_type(X0,set_type)
      | ilf_type(X3,relation_type(X2,X1))
      | ~ ilf_type(X3,relation_type(X2,X0))
      | ~ subset(range_of(X3),X1) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f30,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ilf_type(X1,set_type)
          | ! [X2] :
              ( ! [X3] :
                  ( ~ subset(range_of(X3),X1)
                  | ilf_type(X3,relation_type(X2,X1))
                  | ~ ilf_type(X3,relation_type(X2,X0)) )
              | ~ ilf_type(X2,set_type) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f29]) ).

fof(f29,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ilf_type(X3,relation_type(X2,X1))
                  | ~ subset(range_of(X3),X1)
                  | ~ ilf_type(X3,relation_type(X2,X0)) )
              | ~ ilf_type(X2,set_type) )
          | ~ 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,set_type)
             => ! [X3] :
                  ( ilf_type(X3,relation_type(X2,X0))
                 => ( subset(range_of(X3),X1)
                   => ilf_type(X3,relation_type(X2,X1)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).

fof(f113,plain,
    ~ ilf_type(sK9,relation_type(sK8,sK7)),
    inference(cnf_transformation,[],[f74]) ).

fof(f74,plain,
    ( ~ ilf_type(sK9,relation_type(sK8,sK7))
    & subset(sK6,sK7)
    & ilf_type(sK9,relation_type(sK8,sK6))
    & ilf_type(sK8,set_type)
    & ilf_type(sK7,set_type)
    & ilf_type(sK6,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9])],[f36,f73,f72,f71,f70]) ).

fof(f70,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ~ ilf_type(X3,relation_type(X2,X1))
                    & subset(X0,X1)
                    & ilf_type(X3,relation_type(X2,X0)) )
                & ilf_type(X2,set_type) )
            & ilf_type(X1,set_type) )
        & ilf_type(X0,set_type) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ~ ilf_type(X3,relation_type(X2,X1))
                  & subset(sK6,X1)
                  & ilf_type(X3,relation_type(X2,sK6)) )
              & ilf_type(X2,set_type) )
          & ilf_type(X1,set_type) )
      & ilf_type(sK6,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f71,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ~ ilf_type(X3,relation_type(X2,X1))
                & subset(sK6,X1)
                & ilf_type(X3,relation_type(X2,sK6)) )
            & ilf_type(X2,set_type) )
        & ilf_type(X1,set_type) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ~ ilf_type(X3,relation_type(X2,sK7))
              & subset(sK6,sK7)
              & ilf_type(X3,relation_type(X2,sK6)) )
          & ilf_type(X2,set_type) )
      & ilf_type(sK7,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f72,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ~ ilf_type(X3,relation_type(X2,sK7))
            & subset(sK6,sK7)
            & ilf_type(X3,relation_type(X2,sK6)) )
        & ilf_type(X2,set_type) )
   => ( ? [X3] :
          ( ~ ilf_type(X3,relation_type(sK8,sK7))
          & subset(sK6,sK7)
          & ilf_type(X3,relation_type(sK8,sK6)) )
      & ilf_type(sK8,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f73,plain,
    ( ? [X3] :
        ( ~ ilf_type(X3,relation_type(sK8,sK7))
        & subset(sK6,sK7)
        & ilf_type(X3,relation_type(sK8,sK6)) )
   => ( ~ ilf_type(sK9,relation_type(sK8,sK7))
      & subset(sK6,sK7)
      & ilf_type(sK9,relation_type(sK8,sK6)) ) ),
    introduced(choice_axiom,[]) ).

fof(f36,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ~ ilf_type(X3,relation_type(X2,X1))
                  & subset(X0,X1)
                  & ilf_type(X3,relation_type(X2,X0)) )
              & ilf_type(X2,set_type) )
          & ilf_type(X1,set_type) )
      & ilf_type(X0,set_type) ),
    inference(flattening,[],[f35]) ).

fof(f35,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ~ ilf_type(X3,relation_type(X2,X1))
                  & subset(X0,X1)
                  & ilf_type(X3,relation_type(X2,X0)) )
              & ilf_type(X2,set_type) )
          & ilf_type(X1,set_type) )
      & ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,negated_conjecture,
    ~ ! [X0] :
        ( ilf_type(X0,set_type)
       => ! [X1] :
            ( ilf_type(X1,set_type)
           => ! [X2] :
                ( ilf_type(X2,set_type)
               => ! [X3] :
                    ( ilf_type(X3,relation_type(X2,X0))
                   => ( subset(X0,X1)
                     => ilf_type(X3,relation_type(X2,X1)) ) ) ) ) ),
    inference(negated_conjecture,[],[f23]) ).

fof(f23,conjecture,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,set_type)
             => ! [X3] :
                  ( ilf_type(X3,relation_type(X2,X0))
                 => ( subset(X0,X1)
                   => ilf_type(X3,relation_type(X2,X1)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_16) ).

fof(f111,plain,
    ilf_type(sK9,relation_type(sK8,sK6)),
    inference(cnf_transformation,[],[f74]) ).

fof(f90,plain,
    ! [X0] : ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,axiom,
    ! [X0] : ilf_type(X0,set_type),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22) ).

fof(f158,plain,
    subset(range_of(sK9),sK7),
    inference(unit_resulting_resolution,[],[f112,f90,f90,f90,f142,f129]) ).

fof(f129,plain,
    ! [X2,X0,X1] :
      ( ~ subset(X0,X1)
      | ~ ilf_type(X0,set_type)
      | ~ ilf_type(X2,set_type)
      | subset(X0,X2)
      | ~ ilf_type(X1,set_type)
      | ~ subset(X1,X2) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ilf_type(X1,set_type)
          | ! [X2] :
              ( ~ subset(X0,X1)
              | subset(X0,X2)
              | ~ ilf_type(X2,set_type)
              | ~ subset(X1,X2) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f27]) ).

fof(f27,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( subset(X0,X2)
              | ~ subset(X0,X1)
              | ~ subset(X1,X2)
              | ~ ilf_type(X2,set_type) )
          | ~ 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)
         => ! [X2] :
              ( ilf_type(X2,set_type)
             => ( ( subset(X0,X1)
                  & subset(X1,X2) )
               => subset(X0,X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).

fof(f142,plain,
    subset(range_of(sK9),sK6),
    inference(unit_resulting_resolution,[],[f90,f90,f111,f120]) ).

fof(f120,plain,
    ! [X2,X0,X1] :
      ( ~ ilf_type(X2,relation_type(X0,X1))
      | subset(range_of(X2),X1)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f42]) ).

fof(f42,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ilf_type(X1,set_type)
          | ! [X2] :
              ( ( subset(domain_of(X2),X0)
                & subset(range_of(X2),X1) )
              | ~ ilf_type(X2,relation_type(X0,X1)) ) )
      | ~ 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,relation_type(X0,X1))
             => ( subset(domain_of(X2),X0)
                & subset(range_of(X2),X1) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).

fof(f112,plain,
    subset(sK6,sK7),
    inference(cnf_transformation,[],[f74]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET654+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34  % Computer : n009.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 14:07:35 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.18/0.49  % (18906)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.18/0.49  % (18906)First to succeed.
% 0.18/0.49  % (18915)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.18/0.50  % (18906)Refutation found. Thanks to Tanya!
% 0.18/0.50  % SZS status Theorem for theBenchmark
% 0.18/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.50  % (18906)------------------------------
% 0.18/0.50  % (18906)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.50  % (18906)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.50  % (18906)Termination reason: Refutation
% 0.18/0.50  
% 0.18/0.50  % (18906)Memory used [KB]: 6012
% 0.18/0.50  % (18906)Time elapsed: 0.070 s
% 0.18/0.50  % (18906)Instructions burned: 4 (million)
% 0.18/0.50  % (18906)------------------------------
% 0.18/0.50  % (18906)------------------------------
% 0.18/0.50  % (18898)Success in time 0.152 s
%------------------------------------------------------------------------------