TSTP Solution File: SEU118+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SEU118+1 : TPTP v8.1.0. Released v3.2.0.
% 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 18:31:59 EDT 2022

% Result   : Theorem 0.14s 0.49s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   52 (  12 unt;   3 typ;   0 def)
%            Number of atoms       :  182 (  11 equ)
%            Maximal formula atoms :   15 (   3 avg)
%            Number of connectives :  216 (  83   ~;  75   |;  40   &)
%                                         (   5 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    4 (   0 usr;   3 ari)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   81 (  69   !;  12   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(pred_def_18,type,
    sQ14_eqProxy: ( $int * $int ) > $o ).

tff(pred_def_19,type,
    sQ15_eqProxy: ( $rat * $rat ) > $o ).

tff(pred_def_20,type,
    sQ16_eqProxy: ( $real * $real ) > $o ).

fof(f450,plain,
    $false,
    inference(subsumption_resolution,[],[f447,f217]) ).

fof(f217,plain,
    element(sK9,powerset(sK8)),
    inference(literal_reordering,[],[f146]) ).

fof(f146,plain,
    element(sK9,powerset(sK8)),
    inference(cnf_transformation,[],[f101]) ).

fof(f101,plain,
    ( ~ element(sK9,finite_subsets(sK8))
    & finite(sK8)
    & element(sK9,powerset(sK8)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f99,f100]) ).

fof(f100,plain,
    ( ? [X0,X1] :
        ( ~ element(X1,finite_subsets(X0))
        & finite(X0)
        & element(X1,powerset(X0)) )
   => ( ~ element(sK9,finite_subsets(sK8))
      & finite(sK8)
      & element(sK9,powerset(sK8)) ) ),
    introduced(choice_axiom,[]) ).

fof(f99,plain,
    ? [X0,X1] :
      ( ~ element(X1,finite_subsets(X0))
      & finite(X0)
      & element(X1,powerset(X0)) ),
    inference(rectify,[],[f65]) ).

fof(f65,plain,
    ? [X1,X0] :
      ( ~ element(X0,finite_subsets(X1))
      & finite(X1)
      & element(X0,powerset(X1)) ),
    inference(flattening,[],[f64]) ).

fof(f64,plain,
    ? [X1,X0] :
      ( ~ element(X0,finite_subsets(X1))
      & finite(X1)
      & element(X0,powerset(X1)) ),
    inference(ennf_transformation,[],[f40]) ).

fof(f40,plain,
    ~ ! [X1,X0] :
        ( element(X0,powerset(X1))
       => ( finite(X1)
         => element(X0,finite_subsets(X1)) ) ),
    inference(rectify,[],[f28]) ).

fof(f28,negated_conjecture,
    ~ ! [X1,X0] :
        ( element(X1,powerset(X0))
       => ( finite(X0)
         => element(X1,finite_subsets(X0)) ) ),
    inference(negated_conjecture,[],[f27]) ).

fof(f27,conjecture,
    ! [X1,X0] :
      ( element(X1,powerset(X0))
     => ( finite(X0)
       => element(X1,finite_subsets(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_finsub_1) ).

fof(f447,plain,
    ~ element(sK9,powerset(sK8)),
    inference(resolution,[],[f437,f310]) ).

fof(f310,plain,
    ! [X9] :
      ( finite(X9)
      | ~ element(X9,powerset(sK8)) ),
    inference(resolution,[],[f219,f196]) ).

fof(f196,plain,
    finite(sK8),
    inference(literal_reordering,[],[f147]) ).

fof(f147,plain,
    finite(sK8),
    inference(cnf_transformation,[],[f101]) ).

fof(f219,plain,
    ! [X0,X1] :
      ( ~ finite(X0)
      | ~ element(X1,powerset(X0))
      | finite(X1) ),
    inference(literal_reordering,[],[f166]) ).

fof(f166,plain,
    ! [X0,X1] :
      ( ~ element(X1,powerset(X0))
      | ~ finite(X0)
      | finite(X1) ),
    inference(cnf_transformation,[],[f52]) ).

fof(f52,plain,
    ! [X0] :
      ( ! [X1] :
          ( finite(X1)
          | ~ element(X1,powerset(X0)) )
      | ~ finite(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] :
      ( finite(X0)
     => ! [X1] :
          ( element(X1,powerset(X0))
         => finite(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).

fof(f437,plain,
    ~ finite(sK9),
    inference(subsumption_resolution,[],[f435,f213]) ).

fof(f213,plain,
    ~ element(sK9,finite_subsets(sK8)),
    inference(literal_reordering,[],[f148]) ).

fof(f148,plain,
    ~ element(sK9,finite_subsets(sK8)),
    inference(cnf_transformation,[],[f101]) ).

fof(f435,plain,
    ( ~ finite(sK9)
    | element(sK9,finite_subsets(sK8)) ),
    inference(resolution,[],[f421,f211]) ).

fof(f211,plain,
    ! [X0,X1] :
      ( ~ in(X1,X0)
      | element(X1,X0) ),
    inference(literal_reordering,[],[f123]) ).

fof(f123,plain,
    ! [X0,X1] :
      ( element(X1,X0)
      | ~ in(X1,X0) ),
    inference(cnf_transformation,[],[f58]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( ~ in(X1,X0)
      | element(X1,X0) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( in(X1,X0)
     => element(X1,X0) ),
    inference(rectify,[],[f25]) ).

fof(f25,axiom,
    ! [X1,X0] :
      ( in(X0,X1)
     => element(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).

fof(f421,plain,
    ( in(sK9,finite_subsets(sK8))
    | ~ finite(sK9) ),
    inference(resolution,[],[f332,f217]) ).

fof(f332,plain,
    ! [X2,X1] :
      ( ~ element(X1,powerset(X2))
      | ~ finite(X1)
      | in(X1,finite_subsets(X2)) ),
    inference(resolution,[],[f330,f229]) ).

fof(f229,plain,
    ! [X0,X1] :
      ( subset(X1,X0)
      | ~ element(X1,powerset(X0)) ),
    inference(literal_reordering,[],[f127]) ).

fof(f127,plain,
    ! [X0,X1] :
      ( subset(X1,X0)
      | ~ element(X1,powerset(X0)) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f88,plain,
    ! [X0,X1] :
      ( ( element(X1,powerset(X0))
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ~ element(X1,powerset(X0)) ) ),
    inference(rectify,[],[f87]) ).

fof(f87,plain,
    ! [X1,X0] :
      ( ( element(X0,powerset(X1))
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ~ element(X0,powerset(X1)) ) ),
    inference(nnf_transformation,[],[f29]) ).

fof(f29,axiom,
    ! [X1,X0] :
      ( element(X0,powerset(X1))
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).

fof(f330,plain,
    ! [X3,X1] :
      ( ~ subset(X3,X1)
      | in(X3,finite_subsets(X1))
      | ~ finite(X3) ),
    inference(subsumption_resolution,[],[f183,f179]) ).

fof(f179,plain,
    ! [X0] : preboolean(finite_subsets(X0)),
    inference(literal_reordering,[],[f142]) ).

fof(f142,plain,
    ! [X0] : preboolean(finite_subsets(X0)),
    inference(cnf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0] : preboolean(finite_subsets(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_finsub_1) ).

fof(f183,plain,
    ! [X3,X1] :
      ( ~ preboolean(finite_subsets(X1))
      | ~ subset(X3,X1)
      | ~ finite(X3)
      | in(X3,finite_subsets(X1)) ),
    inference(literal_reordering,[],[f169]) ).

fof(f169,plain,
    ! [X3,X1] :
      ( ~ finite(X3)
      | ~ preboolean(finite_subsets(X1))
      | ~ subset(X3,X1)
      | in(X3,finite_subsets(X1)) ),
    inference(equality_resolution,[],[f138]) ).

fof(f138,plain,
    ! [X3,X0,X1] :
      ( ~ preboolean(X0)
      | in(X3,X0)
      | ~ subset(X3,X1)
      | ~ finite(X3)
      | finite_subsets(X1) != X0 ),
    inference(cnf_transformation,[],[f98]) ).

fof(f98,plain,
    ! [X0,X1] :
      ( ~ preboolean(X0)
      | ( ( finite_subsets(X1) = X0
          | ( ( ~ subset(sK7(X0,X1),X1)
              | ~ finite(sK7(X0,X1))
              | ~ in(sK7(X0,X1),X0) )
            & ( ( subset(sK7(X0,X1),X1)
                & finite(sK7(X0,X1)) )
              | in(sK7(X0,X1),X0) ) ) )
        & ( ! [X3] :
              ( ( in(X3,X0)
                | ~ subset(X3,X1)
                | ~ finite(X3) )
              & ( ( subset(X3,X1)
                  & finite(X3) )
                | ~ in(X3,X0) ) )
          | finite_subsets(X1) != X0 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f96,f97]) ).

fof(f97,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ subset(X2,X1)
            | ~ finite(X2)
            | ~ in(X2,X0) )
          & ( ( subset(X2,X1)
              & finite(X2) )
            | in(X2,X0) ) )
     => ( ( ~ subset(sK7(X0,X1),X1)
          | ~ finite(sK7(X0,X1))
          | ~ in(sK7(X0,X1),X0) )
        & ( ( subset(sK7(X0,X1),X1)
            & finite(sK7(X0,X1)) )
          | in(sK7(X0,X1),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f96,plain,
    ! [X0,X1] :
      ( ~ preboolean(X0)
      | ( ( finite_subsets(X1) = X0
          | ? [X2] :
              ( ( ~ subset(X2,X1)
                | ~ finite(X2)
                | ~ in(X2,X0) )
              & ( ( subset(X2,X1)
                  & finite(X2) )
                | in(X2,X0) ) ) )
        & ( ! [X3] :
              ( ( in(X3,X0)
                | ~ subset(X3,X1)
                | ~ finite(X3) )
              & ( ( subset(X3,X1)
                  & finite(X3) )
                | ~ in(X3,X0) ) )
          | finite_subsets(X1) != X0 ) ) ),
    inference(rectify,[],[f95]) ).

fof(f95,plain,
    ! [X1,X0] :
      ( ~ preboolean(X1)
      | ( ( finite_subsets(X0) = X1
          | ? [X2] :
              ( ( ~ subset(X2,X0)
                | ~ finite(X2)
                | ~ in(X2,X1) )
              & ( ( subset(X2,X0)
                  & finite(X2) )
                | in(X2,X1) ) ) )
        & ( ! [X2] :
              ( ( in(X2,X1)
                | ~ subset(X2,X0)
                | ~ finite(X2) )
              & ( ( subset(X2,X0)
                  & finite(X2) )
                | ~ in(X2,X1) ) )
          | finite_subsets(X0) != X1 ) ) ),
    inference(flattening,[],[f94]) ).

fof(f94,plain,
    ! [X1,X0] :
      ( ~ preboolean(X1)
      | ( ( finite_subsets(X0) = X1
          | ? [X2] :
              ( ( ~ subset(X2,X0)
                | ~ finite(X2)
                | ~ in(X2,X1) )
              & ( ( subset(X2,X0)
                  & finite(X2) )
                | in(X2,X1) ) ) )
        & ( ! [X2] :
              ( ( in(X2,X1)
                | ~ subset(X2,X0)
                | ~ finite(X2) )
              & ( ( subset(X2,X0)
                  & finite(X2) )
                | ~ in(X2,X1) ) )
          | finite_subsets(X0) != X1 ) ) ),
    inference(nnf_transformation,[],[f69]) ).

fof(f69,plain,
    ! [X1,X0] :
      ( ~ preboolean(X1)
      | ( finite_subsets(X0) = X1
      <=> ! [X2] :
            ( in(X2,X1)
          <=> ( subset(X2,X0)
              & finite(X2) ) ) ) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( preboolean(X1)
     => ( finite_subsets(X0) = X1
      <=> ! [X2] :
            ( in(X2,X1)
          <=> ( subset(X2,X0)
              & finite(X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_finsub_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.09  % Problem    : SEU118+1 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.10  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.09/0.30  % Computer : n016.cluster.edu
% 0.09/0.30  % Model    : x86_64 x86_64
% 0.09/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30  % Memory   : 8042.1875MB
% 0.09/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit   : 300
% 0.09/0.30  % WCLimit    : 300
% 0.09/0.30  % DateTime   : Tue Aug 30 15:01:46 EDT 2022
% 0.09/0.30  % CPUTime    : 
% 0.14/0.46  % (7537)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)
% 0.14/0.46  % (7546)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)
% 0.14/0.47  % (7538)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)
% 0.14/0.48  % (7529)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)
% 0.14/0.48  TRYING [1]
% 0.14/0.48  TRYING [2]
% 0.14/0.48  % (7530)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.14/0.48  TRYING [3]
% 0.14/0.48  TRYING [4]
% 0.14/0.48  % (7537)First to succeed.
% 0.14/0.48  % (7545)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)
% 0.14/0.49  % (7538)Also succeeded, but the first one will report.
% 0.14/0.49  % (7537)Refutation found. Thanks to Tanya!
% 0.14/0.49  % SZS status Theorem for theBenchmark
% 0.14/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.49  % (7537)------------------------------
% 0.14/0.49  % (7537)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.14/0.49  % (7537)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.14/0.49  % (7537)Termination reason: Refutation
% 0.14/0.49  
% 0.14/0.49  % (7537)Memory used [KB]: 6012
% 0.14/0.49  % (7537)Time elapsed: 0.014 s
% 0.14/0.49  % (7537)Instructions burned: 12 (million)
% 0.14/0.49  % (7537)------------------------------
% 0.14/0.49  % (7537)------------------------------
% 0.14/0.49  % (7522)Success in time 0.184 s
%------------------------------------------------------------------------------