TSTP Solution File: SEU610_8 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU610_8 : TPTP v8.2.0. Released v8.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n002.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 May 21 04:06:05 EDT 2024

% Result   : Theorem 0.14s 0.36s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   48 (  19 unt;   0 typ;   0 def)
%            Number of atoms       :  231 (  21 equ)
%            Maximal formula atoms :    6 (   4 avg)
%            Number of connectives :  135 (  42   ~;  28   |;  21   &)
%                                         (   4 <=>;  40  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :   99 (  92 fml;   7 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   15 (  12 usr;  10 prp; 0-2 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   80 (  72   !;   8   ?;  24   :)

% Comments : 
%------------------------------------------------------------------------------
tff(f107,plain,
    $false,
    inference(subsumption_resolution,[],[f106,f56]) ).

tff(f56,plain,
    ! [X0: $i] : ~ in(X0,emptyset),
    inference(unit_resulting_resolution,[],[f55,f50]) ).

tff(f50,plain,
    ! [X0: $i] :
      ( ~ in(X0,emptyset)
      | sP3 ),
    inference(cnf_transformation,[],[f50_D]) ).

tff(f50_D,plain,
    ( ! [X0] : ~ in(X0,emptyset)
  <=> ~ sP3 ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP3])]) ).

tff(f55,plain,
    ~ sP3,
    inference(unit_resulting_resolution,[],[f34,f7,f51]) ).

tff(f51,plain,
    ! [X1: $o] :
      ( ~ sP3
      | ~ emptysetE
      | ( $true = (X1) ) ),
    inference(general_splitting,[],[f40,f50_D]) ).

tff(f40,plain,
    ! [X0: $i,X1: $o] :
      ( ( $true = (X1) )
      | ~ in(X0,emptyset)
      | ~ emptysetE ),
    inference(cnf_transformation,[],[f24]) ).

tff(f24,plain,
    ( ! [X0] :
        ( ! [X1: $o] : ( $true = (X1) )
        | ~ in(X0,emptyset) )
    | ~ emptysetE ),
    inference(ennf_transformation,[],[f21]) ).

tff(f21,plain,
    ( emptysetE
   => ! [X0] :
        ( in(X0,emptyset)
       => ! [X1: $o] : ( $true = (X1) ) ) ),
    inference(unused_predicate_definition_removal,[],[f10]) ).

tff(f10,plain,
    ( emptysetE
  <=> ! [X0] :
        ( in(X0,emptyset)
       => ! [X1: $o] : ( $true = (X1) ) ) ),
    inference(fool_elimination,[],[f9]) ).

tff(f9,plain,
    ( emptysetE
    = ( ! [X0] :
          ( in(X0,emptyset)
         => ! [X1: $o] : (X1) ) ) ),
    inference(rectify,[],[f1]) ).

tff(f1,axiom,
    ( emptysetE
    = ( ! [X0] :
          ( in(X0,emptyset)
         => ! [X1: $o] : (X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE) ).

tff(f7,plain,
    $true != $false,
    introduced(fool_axiom,[]) ).

tff(f34,plain,
    emptysetE,
    inference(cnf_transformation,[],[f30]) ).

tff(f30,plain,
    ( ~ subset(sK0,sK1)
    & ( emptyset = setminus(sK0,sK1) )
    & setminusI
    & subsetI2
    & in__Cong
    & emptysetE ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f23,f29]) ).

tff(f29,plain,
    ( ? [X0,X1] :
        ( ~ subset(X0,X1)
        & ( emptyset = setminus(X0,X1) ) )
   => ( ~ subset(sK0,sK1)
      & ( emptyset = setminus(sK0,sK1) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f23,plain,
    ( ? [X0,X1] :
        ( ~ subset(X0,X1)
        & ( emptyset = setminus(X0,X1) ) )
    & setminusI
    & subsetI2
    & in__Cong
    & emptysetE ),
    inference(flattening,[],[f22]) ).

tff(f22,plain,
    ( ? [X0,X1] :
        ( ~ subset(X0,X1)
        & ( emptyset = setminus(X0,X1) ) )
    & setminusI
    & subsetI2
    & in__Cong
    & emptysetE ),
    inference(ennf_transformation,[],[f17]) ).

tff(f17,plain,
    ~ ( emptysetE
     => ( in__Cong
       => ( subsetI2
         => ( setminusI
           => ! [X0,X1] :
                ( ( emptyset = setminus(X0,X1) )
               => subset(X0,X1) ) ) ) ) ),
    inference(rectify,[],[f6]) ).

tff(f6,negated_conjecture,
    ~ ( emptysetE
     => ( in__Cong
       => ( subsetI2
         => ( setminusI
           => ! [X2,X3] :
                ( ( emptyset = setminus(X2,X3) )
               => subset(X2,X3) ) ) ) ) ),
    inference(negated_conjecture,[],[f5]) ).

tff(f5,conjecture,
    ( emptysetE
   => ( in__Cong
     => ( subsetI2
       => ( setminusI
         => ! [X2,X3] :
              ( ( emptyset = setminus(X2,X3) )
             => subset(X2,X3) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset1) ).

tff(f106,plain,
    in(sK2(sK0,sK1),emptyset),
    inference(forward_demodulation,[],[f104,f38]) ).

tff(f38,plain,
    emptyset = setminus(sK0,sK1),
    inference(cnf_transformation,[],[f30]) ).

tff(f104,plain,
    in(sK2(sK0,sK1),setminus(sK0,sK1)),
    inference(unit_resulting_resolution,[],[f63,f62,f54]) ).

tff(f54,plain,
    ! [X2: $i,X0: $i,X1: $i] :
      ( ~ in(X2,X0)
      | in(X2,X1)
      | in(X2,setminus(X0,X1)) ),
    inference(subsumption_resolution,[],[f45,f37]) ).

tff(f37,plain,
    setminusI,
    inference(cnf_transformation,[],[f30]) ).

tff(f45,plain,
    ! [X2: $i,X0: $i,X1: $i] :
      ( in(X2,setminus(X0,X1))
      | in(X2,X1)
      | ~ in(X2,X0)
      | ~ setminusI ),
    inference(cnf_transformation,[],[f28]) ).

tff(f28,plain,
    ( ! [X0,X1,X2] :
        ( in(X2,setminus(X0,X1))
        | in(X2,X1)
        | ~ in(X2,X0) )
    | ~ setminusI ),
    inference(flattening,[],[f27]) ).

tff(f27,plain,
    ( ! [X0,X1,X2] :
        ( in(X2,setminus(X0,X1))
        | in(X2,X1)
        | ~ in(X2,X0) )
    | ~ setminusI ),
    inference(ennf_transformation,[],[f18]) ).

tff(f18,plain,
    ( setminusI
   => ! [X0,X1,X2] :
        ( in(X2,X0)
       => ( ~ in(X2,X1)
         => in(X2,setminus(X0,X1)) ) ) ),
    inference(unused_predicate_definition_removal,[],[f16]) ).

tff(f16,plain,
    ( setminusI
  <=> ! [X0,X1,X2] :
        ( in(X2,X0)
       => ( ~ in(X2,X1)
         => in(X2,setminus(X0,X1)) ) ) ),
    inference(fool_elimination,[],[f15]) ).

tff(f15,plain,
    ( setminusI
    = ( ! [X0,X1,X2] :
          ( in(X2,X0)
         => ( ~ in(X2,X1)
           => in(X2,setminus(X0,X1)) ) ) ) ),
    inference(rectify,[],[f4]) ).

tff(f4,axiom,
    ( setminusI
    = ( ! [X2,X3,X0] :
          ( in(X0,X2)
         => ( ~ in(X0,X3)
           => in(X0,setminus(X2,X3)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI) ).

tff(f62,plain,
    ~ in(sK2(sK0,sK1),sK1),
    inference(unit_resulting_resolution,[],[f39,f52]) ).

tff(f52,plain,
    ! [X0: $i,X1: $i] :
      ( ~ in(sK2(X0,X1),X1)
      | subset(X0,X1) ),
    inference(subsumption_resolution,[],[f44,f36]) ).

tff(f36,plain,
    subsetI2,
    inference(cnf_transformation,[],[f30]) ).

tff(f44,plain,
    ! [X0: $i,X1: $i] :
      ( subset(X0,X1)
      | ~ in(sK2(X0,X1),X1)
      | ~ subsetI2 ),
    inference(cnf_transformation,[],[f33]) ).

tff(f33,plain,
    ( ! [X0,X1] :
        ( subset(X0,X1)
        | ( ~ in(sK2(X0,X1),X1)
          & in(sK2(X0,X1),X0) ) )
    | ~ subsetI2 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f26,f32]) ).

tff(f32,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK2(X0,X1),X1)
        & in(sK2(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

tff(f26,plain,
    ( ! [X0,X1] :
        ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
    | ~ subsetI2 ),
    inference(ennf_transformation,[],[f19]) ).

tff(f19,plain,
    ( subsetI2
   => ! [X0,X1] :
        ( ! [X2] :
            ( in(X2,X0)
           => in(X2,X1) )
       => subset(X0,X1) ) ),
    inference(unused_predicate_definition_removal,[],[f14]) ).

tff(f14,plain,
    ( subsetI2
  <=> ! [X0,X1] :
        ( ! [X2] :
            ( in(X2,X0)
           => in(X2,X1) )
       => subset(X0,X1) ) ),
    inference(fool_elimination,[],[f13]) ).

tff(f13,plain,
    ( subsetI2
    = ( ! [X0,X1] :
          ( ! [X2] :
              ( in(X2,X0)
             => in(X2,X1) )
         => subset(X0,X1) ) ) ),
    inference(rectify,[],[f3]) ).

tff(f3,axiom,
    ( subsetI2
    = ( ! [X2,X3] :
          ( ! [X0] :
              ( in(X0,X2)
             => in(X0,X3) )
         => subset(X2,X3) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2) ).

tff(f39,plain,
    ~ subset(sK0,sK1),
    inference(cnf_transformation,[],[f30]) ).

tff(f63,plain,
    in(sK2(sK0,sK1),sK0),
    inference(unit_resulting_resolution,[],[f39,f53]) ).

tff(f53,plain,
    ! [X0: $i,X1: $i] :
      ( subset(X0,X1)
      | in(sK2(X0,X1),X0) ),
    inference(subsumption_resolution,[],[f43,f36]) ).

tff(f43,plain,
    ! [X0: $i,X1: $i] :
      ( subset(X0,X1)
      | in(sK2(X0,X1),X0)
      | ~ subsetI2 ),
    inference(cnf_transformation,[],[f33]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SEU610_8 : TPTP v8.2.0. Released v8.0.0.
% 0.11/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n002.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sun May 19 17:39:38 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  % (9464)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.36  % (9473)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)
% 0.14/0.36  % (9473)First to succeed.
% 0.14/0.36  % (9473)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-9464"
% 0.14/0.36  % (9473)Refutation found. Thanks to Tanya!
% 0.14/0.36  % SZS status Theorem for theBenchmark
% 0.14/0.36  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.36  % (9473)------------------------------
% 0.14/0.36  % (9473)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.36  % (9473)Termination reason: Refutation
% 0.14/0.36  
% 0.14/0.36  % (9473)Memory used [KB]: 762
% 0.14/0.36  % (9473)Time elapsed: 0.003 s
% 0.14/0.36  % (9473)Instructions burned: 6 (million)
% 0.14/0.36  % (9464)Success in time 0.004 s
%------------------------------------------------------------------------------