TSTP Solution File: SWV116+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SWV116+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n008.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 : Sun May  5 10:28:07 EDT 2024

% Result   : Theorem 0.58s 0.75s
% Output   : Refutation 0.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   84 (   4 unt;   0 def)
%            Number of atoms       :  575 (  79 equ)
%            Maximal formula atoms :   42 (   6 avg)
%            Number of connectives :  733 ( 242   ~; 230   |; 220   &)
%                                         (   8 <=>;  33  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   13 (  11 usr;  10 prp; 0-2 aty)
%            Number of functors    :   18 (  18 usr;  16 con; 0-3 aty)
%            Number of variables   :  146 ( 112   !;  34   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f356,plain,
    $false,
    inference(avatar_sat_refutation,[],[f284,f289,f294,f299,f304,f320,f343,f355]) ).

fof(f355,plain,
    ~ spl9_1,
    inference(avatar_contradiction_clause,[],[f354]) ).

fof(f354,plain,
    ( $false
    | ~ spl9_1 ),
    inference(subsumption_resolution,[],[f353,f275]) ).

fof(f275,plain,
    ( sP0
    | ~ spl9_1 ),
    inference(avatar_component_clause,[],[f273]) ).

fof(f273,plain,
    ( spl9_1
  <=> sP0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_1])]) ).

fof(f353,plain,
    ( ~ sP0
    | ~ spl9_1 ),
    inference(subsumption_resolution,[],[f352,f344]) ).

fof(f344,plain,
    ( leq(n0,sK4)
    | ~ spl9_1 ),
    inference(resolution,[],[f275,f153]) ).

fof(f153,plain,
    ( ~ sP0
    | leq(n0,sK4) ),
    inference(cnf_transformation,[],[f141]) ).

fof(f141,plain,
    ( ( a_select3(q_ds1_filter,sK4,sK5) != a_select3(q_ds1_filter,sK5,sK4)
      & leq(sK5,minus(n6,n1))
      & leq(sK4,minus(n6,n1))
      & leq(n0,sK5)
      & leq(n0,sK4) )
    | ~ sP0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f139,f140]) ).

fof(f140,plain,
    ( ? [X0,X1] :
        ( a_select3(q_ds1_filter,X0,X1) != a_select3(q_ds1_filter,X1,X0)
        & leq(X1,minus(n6,n1))
        & leq(X0,minus(n6,n1))
        & leq(n0,X1)
        & leq(n0,X0) )
   => ( a_select3(q_ds1_filter,sK4,sK5) != a_select3(q_ds1_filter,sK5,sK4)
      & leq(sK5,minus(n6,n1))
      & leq(sK4,minus(n6,n1))
      & leq(n0,sK5)
      & leq(n0,sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f139,plain,
    ( ? [X0,X1] :
        ( a_select3(q_ds1_filter,X0,X1) != a_select3(q_ds1_filter,X1,X0)
        & leq(X1,minus(n6,n1))
        & leq(X0,minus(n6,n1))
        & leq(n0,X1)
        & leq(n0,X0) )
    | ~ sP0 ),
    inference(rectify,[],[f138]) ).

fof(f138,plain,
    ( ? [X14,X15] :
        ( a_select3(q_ds1_filter,X14,X15) != a_select3(q_ds1_filter,X15,X14)
        & leq(X15,minus(n6,n1))
        & leq(X14,minus(n6,n1))
        & leq(n0,X15)
        & leq(n0,X14) )
    | ~ sP0 ),
    inference(nnf_transformation,[],[f131]) ).

fof(f131,plain,
    ( ? [X14,X15] :
        ( a_select3(q_ds1_filter,X14,X15) != a_select3(q_ds1_filter,X15,X14)
        & leq(X15,minus(n6,n1))
        & leq(X14,minus(n6,n1))
        & leq(n0,X15)
        & leq(n0,X14) )
    | ~ sP0 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f352,plain,
    ( ~ leq(n0,sK4)
    | ~ sP0
    | ~ spl9_1 ),
    inference(subsumption_resolution,[],[f351,f345]) ).

fof(f345,plain,
    ( leq(n0,sK5)
    | ~ spl9_1 ),
    inference(resolution,[],[f275,f154]) ).

fof(f154,plain,
    ( ~ sP0
    | leq(n0,sK5) ),
    inference(cnf_transformation,[],[f141]) ).

fof(f351,plain,
    ( ~ leq(n0,sK5)
    | ~ leq(n0,sK4)
    | ~ sP0
    | ~ spl9_1 ),
    inference(subsumption_resolution,[],[f350,f346]) ).

fof(f346,plain,
    ( leq(sK4,minus(n6,n1))
    | ~ spl9_1 ),
    inference(resolution,[],[f275,f155]) ).

fof(f155,plain,
    ( ~ sP0
    | leq(sK4,minus(n6,n1)) ),
    inference(cnf_transformation,[],[f141]) ).

fof(f350,plain,
    ( ~ leq(sK4,minus(n6,n1))
    | ~ leq(n0,sK5)
    | ~ leq(n0,sK4)
    | ~ sP0
    | ~ spl9_1 ),
    inference(subsumption_resolution,[],[f349,f347]) ).

fof(f347,plain,
    ( leq(sK5,minus(n6,n1))
    | ~ spl9_1 ),
    inference(resolution,[],[f275,f156]) ).

fof(f156,plain,
    ( ~ sP0
    | leq(sK5,minus(n6,n1)) ),
    inference(cnf_transformation,[],[f141]) ).

fof(f349,plain,
    ( ~ leq(sK5,minus(n6,n1))
    | ~ leq(sK4,minus(n6,n1))
    | ~ leq(n0,sK5)
    | ~ leq(n0,sK4)
    | ~ sP0 ),
    inference(resolution,[],[f252,f246]) ).

fof(f246,plain,
    ( ~ sQ8_eqProxy(a_select3(q_ds1_filter,sK4,sK5),a_select3(q_ds1_filter,sK5,sK4))
    | ~ sP0 ),
    inference(equality_proxy_replacement,[],[f157,f244]) ).

fof(f244,plain,
    ! [X0,X1] :
      ( sQ8_eqProxy(X0,X1)
    <=> X0 = X1 ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ8_eqProxy])]) ).

fof(f157,plain,
    ( a_select3(q_ds1_filter,sK4,sK5) != a_select3(q_ds1_filter,sK5,sK4)
    | ~ sP0 ),
    inference(cnf_transformation,[],[f141]) ).

fof(f252,plain,
    ! [X10,X11] :
      ( sQ8_eqProxy(a_select3(q_ds1_filter,X10,X11),a_select3(q_ds1_filter,X11,X10))
      | ~ leq(X11,minus(n6,n1))
      | ~ leq(X10,minus(n6,n1))
      | ~ leq(n0,X11)
      | ~ leq(n0,X10) ),
    inference(equality_proxy_replacement,[],[f160,f244]) ).

fof(f160,plain,
    ! [X10,X11] :
      ( a_select3(q_ds1_filter,X10,X11) = a_select3(q_ds1_filter,X11,X10)
      | ~ leq(X11,minus(n6,n1))
      | ~ leq(X10,minus(n6,n1))
      | ~ leq(n0,X11)
      | ~ leq(n0,X10) ),
    inference(cnf_transformation,[],[f144]) ).

fof(f144,plain,
    ( ( ( a_select3(pminus_ds1_filter,sK6,sK7) != a_select3(pminus_ds1_filter,sK7,sK6)
        & leq(sK7,minus(n6,n1))
        & leq(sK6,minus(n6,n1))
        & leq(n0,sK7)
        & leq(n0,sK6) )
      | sP1
      | sP0 )
    & ! [X2] :
        ( ! [X3] :
            ( a_select3(id_ds1_filter,X2,X3) = a_select3(id_ds1_filter,X3,X2)
            | ~ leq(X3,minus(n6,n1))
            | ~ leq(n0,X3) )
        | ~ leq(X2,minus(n6,n1))
        | ~ leq(n0,X2) )
    & ! [X4,X5] :
        ( a_select3(pminus_ds1_filter,X4,X5) = a_select3(pminus_ds1_filter,X5,X4)
        | ~ leq(X5,minus(n6,n1))
        | ~ leq(X4,minus(n6,n1))
        | ~ leq(n0,X5)
        | ~ leq(n0,X4) )
    & ! [X6,X7] :
        ( a_select3(pminus_ds1_filter,X6,X7) = a_select3(pminus_ds1_filter,X7,X6)
        | ~ leq(X7,minus(n6,n1))
        | ~ leq(X6,minus(n6,n1))
        | ~ leq(n0,X7)
        | ~ leq(n0,X6) )
    & ! [X8,X9] :
        ( a_select3(r_ds1_filter,X8,X9) = a_select3(r_ds1_filter,X9,X8)
        | ~ leq(X9,minus(n3,n1))
        | ~ leq(X8,minus(n3,n1))
        | ~ leq(n0,X9)
        | ~ leq(n0,X8) )
    & ! [X10,X11] :
        ( a_select3(q_ds1_filter,X10,X11) = a_select3(q_ds1_filter,X11,X10)
        | ~ leq(X11,minus(n6,n1))
        | ~ leq(X10,minus(n6,n1))
        | ~ leq(n0,X11)
        | ~ leq(n0,X10) )
    & leq(pv5,minus(n999,n1))
    & leq(n0,pv5) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f142,f143]) ).

fof(f143,plain,
    ( ? [X0,X1] :
        ( a_select3(pminus_ds1_filter,X0,X1) != a_select3(pminus_ds1_filter,X1,X0)
        & leq(X1,minus(n6,n1))
        & leq(X0,minus(n6,n1))
        & leq(n0,X1)
        & leq(n0,X0) )
   => ( a_select3(pminus_ds1_filter,sK6,sK7) != a_select3(pminus_ds1_filter,sK7,sK6)
      & leq(sK7,minus(n6,n1))
      & leq(sK6,minus(n6,n1))
      & leq(n0,sK7)
      & leq(n0,sK6) ) ),
    introduced(choice_axiom,[]) ).

fof(f142,plain,
    ( ( ? [X0,X1] :
          ( a_select3(pminus_ds1_filter,X0,X1) != a_select3(pminus_ds1_filter,X1,X0)
          & leq(X1,minus(n6,n1))
          & leq(X0,minus(n6,n1))
          & leq(n0,X1)
          & leq(n0,X0) )
      | sP1
      | sP0 )
    & ! [X2] :
        ( ! [X3] :
            ( a_select3(id_ds1_filter,X2,X3) = a_select3(id_ds1_filter,X3,X2)
            | ~ leq(X3,minus(n6,n1))
            | ~ leq(n0,X3) )
        | ~ leq(X2,minus(n6,n1))
        | ~ leq(n0,X2) )
    & ! [X4,X5] :
        ( a_select3(pminus_ds1_filter,X4,X5) = a_select3(pminus_ds1_filter,X5,X4)
        | ~ leq(X5,minus(n6,n1))
        | ~ leq(X4,minus(n6,n1))
        | ~ leq(n0,X5)
        | ~ leq(n0,X4) )
    & ! [X6,X7] :
        ( a_select3(pminus_ds1_filter,X6,X7) = a_select3(pminus_ds1_filter,X7,X6)
        | ~ leq(X7,minus(n6,n1))
        | ~ leq(X6,minus(n6,n1))
        | ~ leq(n0,X7)
        | ~ leq(n0,X6) )
    & ! [X8,X9] :
        ( a_select3(r_ds1_filter,X8,X9) = a_select3(r_ds1_filter,X9,X8)
        | ~ leq(X9,minus(n3,n1))
        | ~ leq(X8,minus(n3,n1))
        | ~ leq(n0,X9)
        | ~ leq(n0,X8) )
    & ! [X10,X11] :
        ( a_select3(q_ds1_filter,X10,X11) = a_select3(q_ds1_filter,X11,X10)
        | ~ leq(X11,minus(n6,n1))
        | ~ leq(X10,minus(n6,n1))
        | ~ leq(n0,X11)
        | ~ leq(n0,X10) )
    & leq(pv5,minus(n999,n1))
    & leq(n0,pv5) ),
    inference(rectify,[],[f133]) ).

fof(f133,plain,
    ( ( ? [X10,X11] :
          ( a_select3(pminus_ds1_filter,X10,X11) != a_select3(pminus_ds1_filter,X11,X10)
          & leq(X11,minus(n6,n1))
          & leq(X10,minus(n6,n1))
          & leq(n0,X11)
          & leq(n0,X10) )
      | sP1
      | sP0 )
    & ! [X0] :
        ( ! [X1] :
            ( a_select3(id_ds1_filter,X0,X1) = a_select3(id_ds1_filter,X1,X0)
            | ~ leq(X1,minus(n6,n1))
            | ~ leq(n0,X1) )
        | ~ leq(X0,minus(n6,n1))
        | ~ leq(n0,X0) )
    & ! [X2,X3] :
        ( a_select3(pminus_ds1_filter,X2,X3) = a_select3(pminus_ds1_filter,X3,X2)
        | ~ leq(X3,minus(n6,n1))
        | ~ leq(X2,minus(n6,n1))
        | ~ leq(n0,X3)
        | ~ leq(n0,X2) )
    & ! [X4,X5] :
        ( a_select3(pminus_ds1_filter,X4,X5) = a_select3(pminus_ds1_filter,X5,X4)
        | ~ leq(X5,minus(n6,n1))
        | ~ leq(X4,minus(n6,n1))
        | ~ leq(n0,X5)
        | ~ leq(n0,X4) )
    & ! [X6,X7] :
        ( a_select3(r_ds1_filter,X6,X7) = a_select3(r_ds1_filter,X7,X6)
        | ~ leq(X7,minus(n3,n1))
        | ~ leq(X6,minus(n3,n1))
        | ~ leq(n0,X7)
        | ~ leq(n0,X6) )
    & ! [X8,X9] :
        ( a_select3(q_ds1_filter,X8,X9) = a_select3(q_ds1_filter,X9,X8)
        | ~ leq(X9,minus(n6,n1))
        | ~ leq(X8,minus(n6,n1))
        | ~ leq(n0,X9)
        | ~ leq(n0,X8) )
    & leq(pv5,minus(n999,n1))
    & leq(n0,pv5) ),
    inference(definition_folding,[],[f106,f132,f131]) ).

fof(f132,plain,
    ( ? [X12,X13] :
        ( a_select3(r_ds1_filter,X12,X13) != a_select3(r_ds1_filter,X13,X12)
        & leq(X13,minus(n3,n1))
        & leq(X12,minus(n3,n1))
        & leq(n0,X13)
        & leq(n0,X12) )
    | ~ sP1 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f106,plain,
    ( ( ? [X10,X11] :
          ( a_select3(pminus_ds1_filter,X10,X11) != a_select3(pminus_ds1_filter,X11,X10)
          & leq(X11,minus(n6,n1))
          & leq(X10,minus(n6,n1))
          & leq(n0,X11)
          & leq(n0,X10) )
      | ? [X12,X13] :
          ( a_select3(r_ds1_filter,X12,X13) != a_select3(r_ds1_filter,X13,X12)
          & leq(X13,minus(n3,n1))
          & leq(X12,minus(n3,n1))
          & leq(n0,X13)
          & leq(n0,X12) )
      | ? [X14,X15] :
          ( a_select3(q_ds1_filter,X14,X15) != a_select3(q_ds1_filter,X15,X14)
          & leq(X15,minus(n6,n1))
          & leq(X14,minus(n6,n1))
          & leq(n0,X15)
          & leq(n0,X14) ) )
    & ! [X0] :
        ( ! [X1] :
            ( a_select3(id_ds1_filter,X0,X1) = a_select3(id_ds1_filter,X1,X0)
            | ~ leq(X1,minus(n6,n1))
            | ~ leq(n0,X1) )
        | ~ leq(X0,minus(n6,n1))
        | ~ leq(n0,X0) )
    & ! [X2,X3] :
        ( a_select3(pminus_ds1_filter,X2,X3) = a_select3(pminus_ds1_filter,X3,X2)
        | ~ leq(X3,minus(n6,n1))
        | ~ leq(X2,minus(n6,n1))
        | ~ leq(n0,X3)
        | ~ leq(n0,X2) )
    & ! [X4,X5] :
        ( a_select3(pminus_ds1_filter,X4,X5) = a_select3(pminus_ds1_filter,X5,X4)
        | ~ leq(X5,minus(n6,n1))
        | ~ leq(X4,minus(n6,n1))
        | ~ leq(n0,X5)
        | ~ leq(n0,X4) )
    & ! [X6,X7] :
        ( a_select3(r_ds1_filter,X6,X7) = a_select3(r_ds1_filter,X7,X6)
        | ~ leq(X7,minus(n3,n1))
        | ~ leq(X6,minus(n3,n1))
        | ~ leq(n0,X7)
        | ~ leq(n0,X6) )
    & ! [X8,X9] :
        ( a_select3(q_ds1_filter,X8,X9) = a_select3(q_ds1_filter,X9,X8)
        | ~ leq(X9,minus(n6,n1))
        | ~ leq(X8,minus(n6,n1))
        | ~ leq(n0,X9)
        | ~ leq(n0,X8) )
    & leq(pv5,minus(n999,n1))
    & leq(n0,pv5) ),
    inference(flattening,[],[f105]) ).

fof(f105,plain,
    ( ( ? [X10,X11] :
          ( a_select3(pminus_ds1_filter,X10,X11) != a_select3(pminus_ds1_filter,X11,X10)
          & leq(X11,minus(n6,n1))
          & leq(X10,minus(n6,n1))
          & leq(n0,X11)
          & leq(n0,X10) )
      | ? [X12,X13] :
          ( a_select3(r_ds1_filter,X12,X13) != a_select3(r_ds1_filter,X13,X12)
          & leq(X13,minus(n3,n1))
          & leq(X12,minus(n3,n1))
          & leq(n0,X13)
          & leq(n0,X12) )
      | ? [X14,X15] :
          ( a_select3(q_ds1_filter,X14,X15) != a_select3(q_ds1_filter,X15,X14)
          & leq(X15,minus(n6,n1))
          & leq(X14,minus(n6,n1))
          & leq(n0,X15)
          & leq(n0,X14) ) )
    & ! [X0] :
        ( ! [X1] :
            ( a_select3(id_ds1_filter,X0,X1) = a_select3(id_ds1_filter,X1,X0)
            | ~ leq(X1,minus(n6,n1))
            | ~ leq(n0,X1) )
        | ~ leq(X0,minus(n6,n1))
        | ~ leq(n0,X0) )
    & ! [X2,X3] :
        ( a_select3(pminus_ds1_filter,X2,X3) = a_select3(pminus_ds1_filter,X3,X2)
        | ~ leq(X3,minus(n6,n1))
        | ~ leq(X2,minus(n6,n1))
        | ~ leq(n0,X3)
        | ~ leq(n0,X2) )
    & ! [X4,X5] :
        ( a_select3(pminus_ds1_filter,X4,X5) = a_select3(pminus_ds1_filter,X5,X4)
        | ~ leq(X5,minus(n6,n1))
        | ~ leq(X4,minus(n6,n1))
        | ~ leq(n0,X5)
        | ~ leq(n0,X4) )
    & ! [X6,X7] :
        ( a_select3(r_ds1_filter,X6,X7) = a_select3(r_ds1_filter,X7,X6)
        | ~ leq(X7,minus(n3,n1))
        | ~ leq(X6,minus(n3,n1))
        | ~ leq(n0,X7)
        | ~ leq(n0,X6) )
    & ! [X8,X9] :
        ( a_select3(q_ds1_filter,X8,X9) = a_select3(q_ds1_filter,X9,X8)
        | ~ leq(X9,minus(n6,n1))
        | ~ leq(X8,minus(n6,n1))
        | ~ leq(n0,X9)
        | ~ leq(n0,X8) )
    & leq(pv5,minus(n999,n1))
    & leq(n0,pv5) ),
    inference(ennf_transformation,[],[f104]) ).

fof(f104,plain,
    ~ ( ( ! [X0] :
            ( ( leq(X0,minus(n6,n1))
              & leq(n0,X0) )
           => ! [X1] :
                ( ( leq(X1,minus(n6,n1))
                  & leq(n0,X1) )
               => a_select3(id_ds1_filter,X0,X1) = a_select3(id_ds1_filter,X1,X0) ) )
        & ! [X2,X3] :
            ( ( leq(X3,minus(n6,n1))
              & leq(X2,minus(n6,n1))
              & leq(n0,X3)
              & leq(n0,X2) )
           => a_select3(pminus_ds1_filter,X2,X3) = a_select3(pminus_ds1_filter,X3,X2) )
        & ! [X4,X5] :
            ( ( leq(X5,minus(n6,n1))
              & leq(X4,minus(n6,n1))
              & leq(n0,X5)
              & leq(n0,X4) )
           => a_select3(pminus_ds1_filter,X4,X5) = a_select3(pminus_ds1_filter,X5,X4) )
        & ! [X6,X7] :
            ( ( leq(X7,minus(n3,n1))
              & leq(X6,minus(n3,n1))
              & leq(n0,X7)
              & leq(n0,X6) )
           => a_select3(r_ds1_filter,X6,X7) = a_select3(r_ds1_filter,X7,X6) )
        & ! [X8,X9] :
            ( ( leq(X9,minus(n6,n1))
              & leq(X8,minus(n6,n1))
              & leq(n0,X9)
              & leq(n0,X8) )
           => a_select3(q_ds1_filter,X8,X9) = a_select3(q_ds1_filter,X9,X8) )
        & leq(pv5,minus(n999,n1))
        & leq(n0,pv5) )
     => ( ! [X10,X11] :
            ( ( leq(X11,minus(n6,n1))
              & leq(X10,minus(n6,n1))
              & leq(n0,X11)
              & leq(n0,X10) )
           => a_select3(pminus_ds1_filter,X10,X11) = a_select3(pminus_ds1_filter,X11,X10) )
        & ! [X12,X13] :
            ( ( leq(X13,minus(n3,n1))
              & leq(X12,minus(n3,n1))
              & leq(n0,X13)
              & leq(n0,X12) )
           => a_select3(r_ds1_filter,X12,X13) = a_select3(r_ds1_filter,X13,X12) )
        & ! [X14,X15] :
            ( ( leq(X15,minus(n6,n1))
              & leq(X14,minus(n6,n1))
              & leq(n0,X15)
              & leq(n0,X14) )
           => a_select3(q_ds1_filter,X14,X15) = a_select3(q_ds1_filter,X15,X14) ) ) ),
    inference(rectify,[],[f54]) ).

fof(f54,negated_conjecture,
    ~ ( ( ! [X4] :
            ( ( leq(X4,minus(n6,n1))
              & leq(n0,X4) )
           => ! [X10] :
                ( ( leq(X10,minus(n6,n1))
                  & leq(n0,X10) )
               => a_select3(id_ds1_filter,X4,X10) = a_select3(id_ds1_filter,X10,X4) ) )
        & ! [X27,X28] :
            ( ( leq(X28,minus(n6,n1))
              & leq(X27,minus(n6,n1))
              & leq(n0,X28)
              & leq(n0,X27) )
           => a_select3(pminus_ds1_filter,X27,X28) = a_select3(pminus_ds1_filter,X28,X27) )
        & ! [X20,X21] :
            ( ( leq(X21,minus(n6,n1))
              & leq(X20,minus(n6,n1))
              & leq(n0,X21)
              & leq(n0,X20) )
           => a_select3(pminus_ds1_filter,X20,X21) = a_select3(pminus_ds1_filter,X21,X20) )
        & ! [X3,X19] :
            ( ( leq(X19,minus(n3,n1))
              & leq(X3,minus(n3,n1))
              & leq(n0,X19)
              & leq(n0,X3) )
           => a_select3(r_ds1_filter,X3,X19) = a_select3(r_ds1_filter,X19,X3) )
        & ! [X13,X17] :
            ( ( leq(X17,minus(n6,n1))
              & leq(X13,minus(n6,n1))
              & leq(n0,X17)
              & leq(n0,X13) )
           => a_select3(q_ds1_filter,X13,X17) = a_select3(q_ds1_filter,X17,X13) )
        & leq(pv5,minus(n999,n1))
        & leq(n0,pv5) )
     => ( ! [X29,X30] :
            ( ( leq(X30,minus(n6,n1))
              & leq(X29,minus(n6,n1))
              & leq(n0,X30)
              & leq(n0,X29) )
           => a_select3(pminus_ds1_filter,X29,X30) = a_select3(pminus_ds1_filter,X30,X29) )
        & ! [X18,X14] :
            ( ( leq(X14,minus(n3,n1))
              & leq(X18,minus(n3,n1))
              & leq(n0,X14)
              & leq(n0,X18) )
           => a_select3(r_ds1_filter,X18,X14) = a_select3(r_ds1_filter,X14,X18) )
        & ! [X15,X5] :
            ( ( leq(X5,minus(n6,n1))
              & leq(X15,minus(n6,n1))
              & leq(n0,X5)
              & leq(n0,X15) )
           => a_select3(q_ds1_filter,X15,X5) = a_select3(q_ds1_filter,X5,X15) ) ) ),
    inference(negated_conjecture,[],[f53]) ).

fof(f53,conjecture,
    ( ( ! [X4] :
          ( ( leq(X4,minus(n6,n1))
            & leq(n0,X4) )
         => ! [X10] :
              ( ( leq(X10,minus(n6,n1))
                & leq(n0,X10) )
             => a_select3(id_ds1_filter,X4,X10) = a_select3(id_ds1_filter,X10,X4) ) )
      & ! [X27,X28] :
          ( ( leq(X28,minus(n6,n1))
            & leq(X27,minus(n6,n1))
            & leq(n0,X28)
            & leq(n0,X27) )
         => a_select3(pminus_ds1_filter,X27,X28) = a_select3(pminus_ds1_filter,X28,X27) )
      & ! [X20,X21] :
          ( ( leq(X21,minus(n6,n1))
            & leq(X20,minus(n6,n1))
            & leq(n0,X21)
            & leq(n0,X20) )
         => a_select3(pminus_ds1_filter,X20,X21) = a_select3(pminus_ds1_filter,X21,X20) )
      & ! [X3,X19] :
          ( ( leq(X19,minus(n3,n1))
            & leq(X3,minus(n3,n1))
            & leq(n0,X19)
            & leq(n0,X3) )
         => a_select3(r_ds1_filter,X3,X19) = a_select3(r_ds1_filter,X19,X3) )
      & ! [X13,X17] :
          ( ( leq(X17,minus(n6,n1))
            & leq(X13,minus(n6,n1))
            & leq(n0,X17)
            & leq(n0,X13) )
         => a_select3(q_ds1_filter,X13,X17) = a_select3(q_ds1_filter,X17,X13) )
      & leq(pv5,minus(n999,n1))
      & leq(n0,pv5) )
   => ( ! [X29,X30] :
          ( ( leq(X30,minus(n6,n1))
            & leq(X29,minus(n6,n1))
            & leq(n0,X30)
            & leq(n0,X29) )
         => a_select3(pminus_ds1_filter,X29,X30) = a_select3(pminus_ds1_filter,X30,X29) )
      & ! [X18,X14] :
          ( ( leq(X14,minus(n3,n1))
            & leq(X18,minus(n3,n1))
            & leq(n0,X14)
            & leq(n0,X18) )
         => a_select3(r_ds1_filter,X18,X14) = a_select3(r_ds1_filter,X14,X18) )
      & ! [X15,X5] :
          ( ( leq(X5,minus(n6,n1))
            & leq(X15,minus(n6,n1))
            & leq(n0,X5)
            & leq(n0,X15) )
         => a_select3(q_ds1_filter,X15,X5) = a_select3(q_ds1_filter,X5,X15) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.QJK36ftOaL/Vampire---4.8_28989',quaternion_ds1_symm_0009) ).

fof(f343,plain,
    ( ~ spl9_7
    | spl9_3
    | ~ spl9_4
    | ~ spl9_5
    | ~ spl9_6 ),
    inference(avatar_split_clause,[],[f326,f296,f291,f286,f281,f301]) ).

fof(f301,plain,
    ( spl9_7
  <=> leq(n0,sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_7])]) ).

fof(f281,plain,
    ( spl9_3
  <=> sQ8_eqProxy(a_select3(pminus_ds1_filter,sK6,sK7),a_select3(pminus_ds1_filter,sK7,sK6)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_3])]) ).

fof(f286,plain,
    ( spl9_4
  <=> leq(sK7,minus(n6,n1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_4])]) ).

fof(f291,plain,
    ( spl9_5
  <=> leq(sK6,minus(n6,n1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_5])]) ).

fof(f296,plain,
    ( spl9_6
  <=> leq(n0,sK7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_6])]) ).

fof(f326,plain,
    ( ~ leq(n0,sK6)
    | spl9_3
    | ~ spl9_4
    | ~ spl9_5
    | ~ spl9_6 ),
    inference(subsumption_resolution,[],[f325,f298]) ).

fof(f298,plain,
    ( leq(n0,sK7)
    | ~ spl9_6 ),
    inference(avatar_component_clause,[],[f296]) ).

fof(f325,plain,
    ( ~ leq(n0,sK7)
    | ~ leq(n0,sK6)
    | spl9_3
    | ~ spl9_4
    | ~ spl9_5 ),
    inference(subsumption_resolution,[],[f324,f293]) ).

fof(f293,plain,
    ( leq(sK6,minus(n6,n1))
    | ~ spl9_5 ),
    inference(avatar_component_clause,[],[f291]) ).

fof(f324,plain,
    ( ~ leq(sK6,minus(n6,n1))
    | ~ leq(n0,sK7)
    | ~ leq(n0,sK6)
    | spl9_3
    | ~ spl9_4 ),
    inference(subsumption_resolution,[],[f321,f288]) ).

fof(f288,plain,
    ( leq(sK7,minus(n6,n1))
    | ~ spl9_4 ),
    inference(avatar_component_clause,[],[f286]) ).

fof(f321,plain,
    ( ~ leq(sK7,minus(n6,n1))
    | ~ leq(sK6,minus(n6,n1))
    | ~ leq(n0,sK7)
    | ~ leq(n0,sK6)
    | spl9_3 ),
    inference(resolution,[],[f283,f249]) ).

fof(f249,plain,
    ! [X4,X5] :
      ( sQ8_eqProxy(a_select3(pminus_ds1_filter,X4,X5),a_select3(pminus_ds1_filter,X5,X4))
      | ~ leq(X5,minus(n6,n1))
      | ~ leq(X4,minus(n6,n1))
      | ~ leq(n0,X5)
      | ~ leq(n0,X4) ),
    inference(equality_proxy_replacement,[],[f163,f244]) ).

fof(f163,plain,
    ! [X4,X5] :
      ( a_select3(pminus_ds1_filter,X4,X5) = a_select3(pminus_ds1_filter,X5,X4)
      | ~ leq(X5,minus(n6,n1))
      | ~ leq(X4,minus(n6,n1))
      | ~ leq(n0,X5)
      | ~ leq(n0,X4) ),
    inference(cnf_transformation,[],[f144]) ).

fof(f283,plain,
    ( ~ sQ8_eqProxy(a_select3(pminus_ds1_filter,sK6,sK7),a_select3(pminus_ds1_filter,sK7,sK6))
    | spl9_3 ),
    inference(avatar_component_clause,[],[f281]) ).

fof(f320,plain,
    ~ spl9_2,
    inference(avatar_split_clause,[],[f319,f277]) ).

fof(f277,plain,
    ( spl9_2
  <=> sP1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_2])]) ).

fof(f319,plain,
    ~ sP1,
    inference(subsumption_resolution,[],[f318,f148]) ).

fof(f148,plain,
    ( ~ sP1
    | leq(n0,sK2) ),
    inference(cnf_transformation,[],[f137]) ).

fof(f137,plain,
    ( ( a_select3(r_ds1_filter,sK2,sK3) != a_select3(r_ds1_filter,sK3,sK2)
      & leq(sK3,minus(n3,n1))
      & leq(sK2,minus(n3,n1))
      & leq(n0,sK3)
      & leq(n0,sK2) )
    | ~ sP1 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f135,f136]) ).

fof(f136,plain,
    ( ? [X0,X1] :
        ( a_select3(r_ds1_filter,X0,X1) != a_select3(r_ds1_filter,X1,X0)
        & leq(X1,minus(n3,n1))
        & leq(X0,minus(n3,n1))
        & leq(n0,X1)
        & leq(n0,X0) )
   => ( a_select3(r_ds1_filter,sK2,sK3) != a_select3(r_ds1_filter,sK3,sK2)
      & leq(sK3,minus(n3,n1))
      & leq(sK2,minus(n3,n1))
      & leq(n0,sK3)
      & leq(n0,sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f135,plain,
    ( ? [X0,X1] :
        ( a_select3(r_ds1_filter,X0,X1) != a_select3(r_ds1_filter,X1,X0)
        & leq(X1,minus(n3,n1))
        & leq(X0,minus(n3,n1))
        & leq(n0,X1)
        & leq(n0,X0) )
    | ~ sP1 ),
    inference(rectify,[],[f134]) ).

fof(f134,plain,
    ( ? [X12,X13] :
        ( a_select3(r_ds1_filter,X12,X13) != a_select3(r_ds1_filter,X13,X12)
        & leq(X13,minus(n3,n1))
        & leq(X12,minus(n3,n1))
        & leq(n0,X13)
        & leq(n0,X12) )
    | ~ sP1 ),
    inference(nnf_transformation,[],[f132]) ).

fof(f318,plain,
    ( ~ leq(n0,sK2)
    | ~ sP1 ),
    inference(subsumption_resolution,[],[f317,f149]) ).

fof(f149,plain,
    ( ~ sP1
    | leq(n0,sK3) ),
    inference(cnf_transformation,[],[f137]) ).

fof(f317,plain,
    ( ~ leq(n0,sK3)
    | ~ leq(n0,sK2)
    | ~ sP1 ),
    inference(subsumption_resolution,[],[f316,f150]) ).

fof(f150,plain,
    ( ~ sP1
    | leq(sK2,minus(n3,n1)) ),
    inference(cnf_transformation,[],[f137]) ).

fof(f316,plain,
    ( ~ leq(sK2,minus(n3,n1))
    | ~ leq(n0,sK3)
    | ~ leq(n0,sK2)
    | ~ sP1 ),
    inference(subsumption_resolution,[],[f309,f151]) ).

fof(f151,plain,
    ( ~ sP1
    | leq(sK3,minus(n3,n1)) ),
    inference(cnf_transformation,[],[f137]) ).

fof(f309,plain,
    ( ~ leq(sK3,minus(n3,n1))
    | ~ leq(sK2,minus(n3,n1))
    | ~ leq(n0,sK3)
    | ~ leq(n0,sK2)
    | ~ sP1 ),
    inference(resolution,[],[f251,f245]) ).

fof(f245,plain,
    ( ~ sQ8_eqProxy(a_select3(r_ds1_filter,sK2,sK3),a_select3(r_ds1_filter,sK3,sK2))
    | ~ sP1 ),
    inference(equality_proxy_replacement,[],[f152,f244]) ).

fof(f152,plain,
    ( a_select3(r_ds1_filter,sK2,sK3) != a_select3(r_ds1_filter,sK3,sK2)
    | ~ sP1 ),
    inference(cnf_transformation,[],[f137]) ).

fof(f251,plain,
    ! [X8,X9] :
      ( sQ8_eqProxy(a_select3(r_ds1_filter,X8,X9),a_select3(r_ds1_filter,X9,X8))
      | ~ leq(X9,minus(n3,n1))
      | ~ leq(X8,minus(n3,n1))
      | ~ leq(n0,X9)
      | ~ leq(n0,X8) ),
    inference(equality_proxy_replacement,[],[f161,f244]) ).

fof(f161,plain,
    ! [X8,X9] :
      ( a_select3(r_ds1_filter,X8,X9) = a_select3(r_ds1_filter,X9,X8)
      | ~ leq(X9,minus(n3,n1))
      | ~ leq(X8,minus(n3,n1))
      | ~ leq(n0,X9)
      | ~ leq(n0,X8) ),
    inference(cnf_transformation,[],[f144]) ).

fof(f304,plain,
    ( spl9_1
    | spl9_2
    | spl9_7 ),
    inference(avatar_split_clause,[],[f165,f301,f277,f273]) ).

fof(f165,plain,
    ( leq(n0,sK6)
    | sP1
    | sP0 ),
    inference(cnf_transformation,[],[f144]) ).

fof(f299,plain,
    ( spl9_1
    | spl9_2
    | spl9_6 ),
    inference(avatar_split_clause,[],[f166,f296,f277,f273]) ).

fof(f166,plain,
    ( leq(n0,sK7)
    | sP1
    | sP0 ),
    inference(cnf_transformation,[],[f144]) ).

fof(f294,plain,
    ( spl9_1
    | spl9_2
    | spl9_5 ),
    inference(avatar_split_clause,[],[f167,f291,f277,f273]) ).

fof(f167,plain,
    ( leq(sK6,minus(n6,n1))
    | sP1
    | sP0 ),
    inference(cnf_transformation,[],[f144]) ).

fof(f289,plain,
    ( spl9_1
    | spl9_2
    | spl9_4 ),
    inference(avatar_split_clause,[],[f168,f286,f277,f273]) ).

fof(f168,plain,
    ( leq(sK7,minus(n6,n1))
    | sP1
    | sP0 ),
    inference(cnf_transformation,[],[f144]) ).

fof(f284,plain,
    ( spl9_1
    | spl9_2
    | ~ spl9_3 ),
    inference(avatar_split_clause,[],[f247,f281,f277,f273]) ).

fof(f247,plain,
    ( ~ sQ8_eqProxy(a_select3(pminus_ds1_filter,sK6,sK7),a_select3(pminus_ds1_filter,sK7,sK6))
    | sP1
    | sP0 ),
    inference(equality_proxy_replacement,[],[f169,f244]) ).

fof(f169,plain,
    ( a_select3(pminus_ds1_filter,sK6,sK7) != a_select3(pminus_ds1_filter,sK7,sK6)
    | sP1
    | sP0 ),
    inference(cnf_transformation,[],[f144]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SWV116+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.16/0.36  % Computer : n008.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit   : 300
% 0.16/0.36  % WCLimit    : 300
% 0.16/0.36  % DateTime   : Fri May  3 20:57:38 EDT 2024
% 0.16/0.36  % CPUTime    : 
% 0.16/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.16/0.37  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.QJK36ftOaL/Vampire---4.8_28989
% 0.58/0.75  % (29360)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2996ds/56Mi)
% 0.58/0.75  % (29355)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.58/0.75  % (29353)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2996ds/34Mi)
% 0.58/0.75  % (29356)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.58/0.75  % (29354)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2996ds/51Mi)
% 0.58/0.75  % (29358)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.58/0.75  % (29357)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2996ds/34Mi)
% 0.58/0.75  % (29359)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2996ds/83Mi)
% 0.58/0.75  % (29360)First to succeed.
% 0.58/0.75  % (29360)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-29198"
% 0.58/0.75  % (29360)Refutation found. Thanks to Tanya!
% 0.58/0.75  % SZS status Theorem for Vampire---4
% 0.58/0.75  % SZS output start Proof for Vampire---4
% See solution above
% 0.58/0.75  % (29360)------------------------------
% 0.58/0.75  % (29360)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.75  % (29360)Termination reason: Refutation
% 0.58/0.75  
% 0.58/0.75  % (29360)Memory used [KB]: 1186
% 0.58/0.75  % (29360)Time elapsed: 0.005 s
% 0.58/0.75  % (29360)Instructions burned: 12 (million)
% 0.58/0.75  % (29198)Success in time 0.376 s
% 0.58/0.75  % Vampire---4.8 exiting
%------------------------------------------------------------------------------