TSTP Solution File: COM017+4 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : COM017+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n023.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 May  1 02:13:13 EDT 2024

% Result   : Theorem 0.62s 0.81s
% Output   : Refutation 0.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   59 (   8 unt;   1 typ;   0 def)
%            Number of atoms       :  970 (  29 equ)
%            Maximal formula atoms :   30 (  16 avg)
%            Number of connectives :  619 ( 200   ~; 215   |; 191   &)
%                                         (   3 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   8 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :  493 ( 493 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    2 (   1   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :   25 (  23 usr;  12 prp; 0-3 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :  116 (  81   !;  34   ?;  30   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
tff(pred_def_18,type,
    sQ24_eqProxy: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

tff(f478,plain,
    $false,
    inference(avatar_sat_refutation,[],[f350,f465,f472,f477]) ).

tff(f477,plain,
    ~ spl25_26,
    inference(avatar_contradiction_clause,[],[f476]) ).

tff(f476,plain,
    ( $false
    | ~ spl25_26 ),
    inference(subsumption_resolution,[],[f475,f125]) ).

tff(f125,plain,
    aElement0(xa),
    inference(cnf_transformation,[],[f17]) ).

tff(f17,axiom,
    ( aElement0(xc)
    & aElement0(xb)
    & aElement0(xa) ),
    file('/export/starexec/sandbox/tmp/tmp.6DYLCjgnpJ/Vampire---4.8_25750',m__731) ).

tff(f475,plain,
    ( ~ aElement0(xa)
    | ~ spl25_26 ),
    inference(subsumption_resolution,[],[f474,f159]) ).

tff(f159,plain,
    aReductOfIn0(xu,xa,xR),
    inference(cnf_transformation,[],[f85]) ).

tff(f85,plain,
    ( sdtmndtasgtdt0(xu,xR,xb)
    & ( ( sdtmndtplgtdt0(xu,xR,xb)
        & ( ( sdtmndtplgtdt0(sK15,xR,xb)
            & aReductOfIn0(sK15,xu,xR)
            & aElement0(sK15) )
          | aReductOfIn0(xb,xu,xR) ) )
      | ( xb = xu ) )
    & aReductOfIn0(xu,xa,xR)
    & aElement0(xu) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f20,f84]) ).

tff(f84,plain,
    ( ? [X0] :
        ( sdtmndtplgtdt0(X0,xR,xb)
        & aReductOfIn0(X0,xu,xR)
        & aElement0(X0) )
   => ( sdtmndtplgtdt0(sK15,xR,xb)
      & aReductOfIn0(sK15,xu,xR)
      & aElement0(sK15) ) ),
    introduced(choice_axiom,[]) ).

tff(f20,axiom,
    ( sdtmndtasgtdt0(xu,xR,xb)
    & ( ( sdtmndtplgtdt0(xu,xR,xb)
        & ( ? [X0] :
              ( sdtmndtplgtdt0(X0,xR,xb)
              & aReductOfIn0(X0,xu,xR)
              & aElement0(X0) )
          | aReductOfIn0(xb,xu,xR) ) )
      | ( xb = xu ) )
    & aReductOfIn0(xu,xa,xR)
    & aElement0(xu) ),
    file('/export/starexec/sandbox/tmp/tmp.6DYLCjgnpJ/Vampire---4.8_25750',m__755) ).

tff(f474,plain,
    ( ~ aReductOfIn0(xu,xa,xR)
    | ~ aElement0(xa)
    | ~ spl25_26 ),
    inference(resolution,[],[f464,f166]) ).

tff(f166,plain,
    aReductOfIn0(xv,xa,xR),
    inference(cnf_transformation,[],[f87]) ).

tff(f87,plain,
    ( sdtmndtasgtdt0(xv,xR,xc)
    & ( ( sdtmndtplgtdt0(xv,xR,xc)
        & ( ( sdtmndtplgtdt0(sK16,xR,xc)
            & aReductOfIn0(sK16,xv,xR)
            & aElement0(sK16) )
          | aReductOfIn0(xc,xv,xR) ) )
      | ( xc = xv ) )
    & aReductOfIn0(xv,xa,xR)
    & aElement0(xv) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f21,f86]) ).

tff(f86,plain,
    ( ? [X0] :
        ( sdtmndtplgtdt0(X0,xR,xc)
        & aReductOfIn0(X0,xv,xR)
        & aElement0(X0) )
   => ( sdtmndtplgtdt0(sK16,xR,xc)
      & aReductOfIn0(sK16,xv,xR)
      & aElement0(sK16) ) ),
    introduced(choice_axiom,[]) ).

tff(f21,axiom,
    ( sdtmndtasgtdt0(xv,xR,xc)
    & ( ( sdtmndtplgtdt0(xv,xR,xc)
        & ( ? [X0] :
              ( sdtmndtplgtdt0(X0,xR,xc)
              & aReductOfIn0(X0,xv,xR)
              & aElement0(X0) )
          | aReductOfIn0(xc,xv,xR) ) )
      | ( xc = xv ) )
    & aReductOfIn0(xv,xa,xR)
    & aElement0(xv) ),
    file('/export/starexec/sandbox/tmp/tmp.6DYLCjgnpJ/Vampire---4.8_25750',m__779) ).

tff(f464,plain,
    ( ! [X1: $i] :
        ( ~ aReductOfIn0(xv,X1,xR)
        | ~ aReductOfIn0(xu,X1,xR)
        | ~ aElement0(X1) )
    | ~ spl25_26 ),
    inference(avatar_component_clause,[],[f463]) ).

tff(f463,plain,
    ( spl25_26
  <=> ! [X1] :
        ( ~ aReductOfIn0(xu,X1,xR)
        | ~ aReductOfIn0(xv,X1,xR)
        | ~ aElement0(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl25_26])]) ).

tff(f472,plain,
    ( spl25_26
    | ~ spl25_21
    | spl25_25 ),
    inference(avatar_split_clause,[],[f471,f459,f340,f463]) ).

tff(f340,plain,
    ( spl25_21
  <=> aElement0(xv) ),
    introduced(avatar_definition,[new_symbols(naming,[spl25_21])]) ).

tff(f459,plain,
    ( spl25_25
  <=> aElement0(sK8(xu,xv)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl25_25])]) ).

tff(f471,plain,
    ( ! [X0: $i] :
        ( ~ aReductOfIn0(xv,X0,xR)
        | ~ aReductOfIn0(xu,X0,xR)
        | ~ aElement0(X0) )
    | ~ spl25_21
    | spl25_25 ),
    inference(subsumption_resolution,[],[f470,f158]) ).

tff(f158,plain,
    aElement0(xu),
    inference(cnf_transformation,[],[f85]) ).

tff(f470,plain,
    ( ! [X0: $i] :
        ( ~ aReductOfIn0(xv,X0,xR)
        | ~ aReductOfIn0(xu,X0,xR)
        | ~ aElement0(xu)
        | ~ aElement0(X0) )
    | ~ spl25_21
    | spl25_25 ),
    inference(subsumption_resolution,[],[f468,f341]) ).

tff(f341,plain,
    ( aElement0(xv)
    | ~ spl25_21 ),
    inference(avatar_component_clause,[],[f340]) ).

tff(f468,plain,
    ( ! [X0: $i] :
        ( ~ aReductOfIn0(xv,X0,xR)
        | ~ aReductOfIn0(xu,X0,xR)
        | ~ aElement0(xv)
        | ~ aElement0(xu)
        | ~ aElement0(X0) )
    | spl25_25 ),
    inference(resolution,[],[f461,f112]) ).

tff(f112,plain,
    ! [X3: $i,X4: $i,X5: $i] :
      ( aElement0(sK8(X4,X5))
      | ~ aReductOfIn0(X5,X3,xR)
      | ~ aReductOfIn0(X4,X3,xR)
      | ~ aElement0(X5)
      | ~ aElement0(X4)
      | ~ aElement0(X3) ),
    inference(cnf_transformation,[],[f69]) ).

tff(f69,plain,
    ( isTerminating0(xR)
    & ! [X0,X1] :
        ( iLess0(X1,X0)
        | ( ~ sdtmndtplgtdt0(X0,xR,X1)
          & ! [X2] :
              ( ~ sdtmndtplgtdt0(X2,xR,X1)
              | ~ aReductOfIn0(X2,X0,xR)
              | ~ aElement0(X2) )
          & ~ aReductOfIn0(X1,X0,xR) )
        | ~ aElement0(X1)
        | ~ aElement0(X0) )
    & isLocallyConfluent0(xR)
    & ! [X3,X4,X5] :
        ( ( sdtmndtasgtdt0(X5,xR,sK8(X4,X5))
          & ( ( sdtmndtplgtdt0(X5,xR,sK8(X4,X5))
              & ( ( sdtmndtplgtdt0(sK9(X4,X5),xR,sK8(X4,X5))
                  & aReductOfIn0(sK9(X4,X5),X5,xR)
                  & aElement0(sK9(X4,X5)) )
                | aReductOfIn0(sK8(X4,X5),X5,xR) ) )
            | ( sK8(X4,X5) = X5 ) )
          & sdtmndtasgtdt0(X4,xR,sK8(X4,X5))
          & sP0(sK8(X4,X5),X4)
          & aElement0(sK8(X4,X5)) )
        | ~ aReductOfIn0(X5,X3,xR)
        | ~ aReductOfIn0(X4,X3,xR)
        | ~ aElement0(X5)
        | ~ aElement0(X4)
        | ~ aElement0(X3) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f53,f68,f67]) ).

tff(f67,plain,
    ! [X4,X5] :
      ( ? [X6] :
          ( sdtmndtasgtdt0(X5,xR,X6)
          & ( ( sdtmndtplgtdt0(X5,xR,X6)
              & ( ? [X7] :
                    ( sdtmndtplgtdt0(X7,xR,X6)
                    & aReductOfIn0(X7,X5,xR)
                    & aElement0(X7) )
                | aReductOfIn0(X6,X5,xR) ) )
            | ( X5 = X6 ) )
          & sdtmndtasgtdt0(X4,xR,X6)
          & sP0(X6,X4)
          & aElement0(X6) )
     => ( sdtmndtasgtdt0(X5,xR,sK8(X4,X5))
        & ( ( sdtmndtplgtdt0(X5,xR,sK8(X4,X5))
            & ( ? [X7] :
                  ( sdtmndtplgtdt0(X7,xR,sK8(X4,X5))
                  & aReductOfIn0(X7,X5,xR)
                  & aElement0(X7) )
              | aReductOfIn0(sK8(X4,X5),X5,xR) ) )
          | ( sK8(X4,X5) = X5 ) )
        & sdtmndtasgtdt0(X4,xR,sK8(X4,X5))
        & sP0(sK8(X4,X5),X4)
        & aElement0(sK8(X4,X5)) ) ),
    introduced(choice_axiom,[]) ).

tff(f68,plain,
    ! [X4,X5] :
      ( ? [X7] :
          ( sdtmndtplgtdt0(X7,xR,sK8(X4,X5))
          & aReductOfIn0(X7,X5,xR)
          & aElement0(X7) )
     => ( sdtmndtplgtdt0(sK9(X4,X5),xR,sK8(X4,X5))
        & aReductOfIn0(sK9(X4,X5),X5,xR)
        & aElement0(sK9(X4,X5)) ) ),
    introduced(choice_axiom,[]) ).

tff(f53,plain,
    ( isTerminating0(xR)
    & ! [X0,X1] :
        ( iLess0(X1,X0)
        | ( ~ sdtmndtplgtdt0(X0,xR,X1)
          & ! [X2] :
              ( ~ sdtmndtplgtdt0(X2,xR,X1)
              | ~ aReductOfIn0(X2,X0,xR)
              | ~ aElement0(X2) )
          & ~ aReductOfIn0(X1,X0,xR) )
        | ~ aElement0(X1)
        | ~ aElement0(X0) )
    & isLocallyConfluent0(xR)
    & ! [X3,X4,X5] :
        ( ? [X6] :
            ( sdtmndtasgtdt0(X5,xR,X6)
            & ( ( sdtmndtplgtdt0(X5,xR,X6)
                & ( ? [X7] :
                      ( sdtmndtplgtdt0(X7,xR,X6)
                      & aReductOfIn0(X7,X5,xR)
                      & aElement0(X7) )
                  | aReductOfIn0(X6,X5,xR) ) )
              | ( X5 = X6 ) )
            & sdtmndtasgtdt0(X4,xR,X6)
            & sP0(X6,X4)
            & aElement0(X6) )
        | ~ aReductOfIn0(X5,X3,xR)
        | ~ aReductOfIn0(X4,X3,xR)
        | ~ aElement0(X5)
        | ~ aElement0(X4)
        | ~ aElement0(X3) ) ),
    inference(definition_folding,[],[f34,f52]) ).

tff(f52,plain,
    ! [X6,X4] :
      ( ( sdtmndtplgtdt0(X4,xR,X6)
        & ( ? [X8] :
              ( sdtmndtplgtdt0(X8,xR,X6)
              & aReductOfIn0(X8,X4,xR)
              & aElement0(X8) )
          | aReductOfIn0(X6,X4,xR) ) )
      | ( X4 = X6 )
      | ~ sP0(X6,X4) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

tff(f34,plain,
    ( isTerminating0(xR)
    & ! [X0,X1] :
        ( iLess0(X1,X0)
        | ( ~ sdtmndtplgtdt0(X0,xR,X1)
          & ! [X2] :
              ( ~ sdtmndtplgtdt0(X2,xR,X1)
              | ~ aReductOfIn0(X2,X0,xR)
              | ~ aElement0(X2) )
          & ~ aReductOfIn0(X1,X0,xR) )
        | ~ aElement0(X1)
        | ~ aElement0(X0) )
    & isLocallyConfluent0(xR)
    & ! [X3,X4,X5] :
        ( ? [X6] :
            ( sdtmndtasgtdt0(X5,xR,X6)
            & ( ( sdtmndtplgtdt0(X5,xR,X6)
                & ( ? [X7] :
                      ( sdtmndtplgtdt0(X7,xR,X6)
                      & aReductOfIn0(X7,X5,xR)
                      & aElement0(X7) )
                  | aReductOfIn0(X6,X5,xR) ) )
              | ( X5 = X6 ) )
            & sdtmndtasgtdt0(X4,xR,X6)
            & ( ( sdtmndtplgtdt0(X4,xR,X6)
                & ( ? [X8] :
                      ( sdtmndtplgtdt0(X8,xR,X6)
                      & aReductOfIn0(X8,X4,xR)
                      & aElement0(X8) )
                  | aReductOfIn0(X6,X4,xR) ) )
              | ( X4 = X6 ) )
            & aElement0(X6) )
        | ~ aReductOfIn0(X5,X3,xR)
        | ~ aReductOfIn0(X4,X3,xR)
        | ~ aElement0(X5)
        | ~ aElement0(X4)
        | ~ aElement0(X3) ) ),
    inference(flattening,[],[f33]) ).

tff(f33,plain,
    ( isTerminating0(xR)
    & ! [X0,X1] :
        ( iLess0(X1,X0)
        | ( ~ sdtmndtplgtdt0(X0,xR,X1)
          & ! [X2] :
              ( ~ sdtmndtplgtdt0(X2,xR,X1)
              | ~ aReductOfIn0(X2,X0,xR)
              | ~ aElement0(X2) )
          & ~ aReductOfIn0(X1,X0,xR) )
        | ~ aElement0(X1)
        | ~ aElement0(X0) )
    & isLocallyConfluent0(xR)
    & ! [X3,X4,X5] :
        ( ? [X6] :
            ( sdtmndtasgtdt0(X5,xR,X6)
            & ( ( sdtmndtplgtdt0(X5,xR,X6)
                & ( ? [X7] :
                      ( sdtmndtplgtdt0(X7,xR,X6)
                      & aReductOfIn0(X7,X5,xR)
                      & aElement0(X7) )
                  | aReductOfIn0(X6,X5,xR) ) )
              | ( X5 = X6 ) )
            & sdtmndtasgtdt0(X4,xR,X6)
            & ( ( sdtmndtplgtdt0(X4,xR,X6)
                & ( ? [X8] :
                      ( sdtmndtplgtdt0(X8,xR,X6)
                      & aReductOfIn0(X8,X4,xR)
                      & aElement0(X8) )
                  | aReductOfIn0(X6,X4,xR) ) )
              | ( X4 = X6 ) )
            & aElement0(X6) )
        | ~ aReductOfIn0(X5,X3,xR)
        | ~ aReductOfIn0(X4,X3,xR)
        | ~ aElement0(X5)
        | ~ aElement0(X4)
        | ~ aElement0(X3) ) ),
    inference(ennf_transformation,[],[f24]) ).

tff(f24,plain,
    ( isTerminating0(xR)
    & ! [X0,X1] :
        ( ( aElement0(X1)
          & aElement0(X0) )
       => ( ( sdtmndtplgtdt0(X0,xR,X1)
            | ? [X2] :
                ( sdtmndtplgtdt0(X2,xR,X1)
                & aReductOfIn0(X2,X0,xR)
                & aElement0(X2) )
            | aReductOfIn0(X1,X0,xR) )
         => iLess0(X1,X0) ) )
    & isLocallyConfluent0(xR)
    & ! [X3,X4,X5] :
        ( ( aReductOfIn0(X5,X3,xR)
          & aReductOfIn0(X4,X3,xR)
          & aElement0(X5)
          & aElement0(X4)
          & aElement0(X3) )
       => ? [X6] :
            ( sdtmndtasgtdt0(X5,xR,X6)
            & ( ( sdtmndtplgtdt0(X5,xR,X6)
                & ( ? [X7] :
                      ( sdtmndtplgtdt0(X7,xR,X6)
                      & aReductOfIn0(X7,X5,xR)
                      & aElement0(X7) )
                  | aReductOfIn0(X6,X5,xR) ) )
              | ( X5 = X6 ) )
            & sdtmndtasgtdt0(X4,xR,X6)
            & ( ( sdtmndtplgtdt0(X4,xR,X6)
                & ( ? [X8] :
                      ( sdtmndtplgtdt0(X8,xR,X6)
                      & aReductOfIn0(X8,X4,xR)
                      & aElement0(X8) )
                  | aReductOfIn0(X6,X4,xR) ) )
              | ( X4 = X6 ) )
            & aElement0(X6) ) ) ),
    inference(rectify,[],[f16]) ).

tff(f16,axiom,
    ( isTerminating0(xR)
    & ! [X0,X1] :
        ( ( aElement0(X1)
          & aElement0(X0) )
       => ( ( sdtmndtplgtdt0(X0,xR,X1)
            | ? [X2] :
                ( sdtmndtplgtdt0(X2,xR,X1)
                & aReductOfIn0(X2,X0,xR)
                & aElement0(X2) )
            | aReductOfIn0(X1,X0,xR) )
         => iLess0(X1,X0) ) )
    & isLocallyConfluent0(xR)
    & ! [X0,X1,X2] :
        ( ( aReductOfIn0(X2,X0,xR)
          & aReductOfIn0(X1,X0,xR)
          & aElement0(X2)
          & aElement0(X1)
          & aElement0(X0) )
       => ? [X3] :
            ( sdtmndtasgtdt0(X2,xR,X3)
            & ( ( sdtmndtplgtdt0(X2,xR,X3)
                & ( ? [X4] :
                      ( sdtmndtplgtdt0(X4,xR,X3)
                      & aReductOfIn0(X4,X2,xR)
                      & aElement0(X4) )
                  | aReductOfIn0(X3,X2,xR) ) )
              | ( X2 = X3 ) )
            & sdtmndtasgtdt0(X1,xR,X3)
            & ( ( sdtmndtplgtdt0(X1,xR,X3)
                & ( ? [X4] :
                      ( sdtmndtplgtdt0(X4,xR,X3)
                      & aReductOfIn0(X4,X1,xR)
                      & aElement0(X4) )
                  | aReductOfIn0(X3,X1,xR) ) )
              | ( X1 = X3 ) )
            & aElement0(X3) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.6DYLCjgnpJ/Vampire---4.8_25750',m__656_01) ).

tff(f461,plain,
    ( ~ aElement0(sK8(xu,xv))
    | spl25_25 ),
    inference(avatar_component_clause,[],[f459]) ).

tff(f465,plain,
    ( ~ spl25_25
    | spl25_26
    | spl25_26
    | ~ spl25_21 ),
    inference(avatar_split_clause,[],[f457,f340,f463,f463,f459]) ).

tff(f457,plain,
    ( ! [X0: $i,X1: $i] :
        ( ~ aReductOfIn0(xu,X0,xR)
        | ~ aElement0(X0)
        | ~ aReductOfIn0(xv,X0,xR)
        | ~ aReductOfIn0(xu,X1,xR)
        | ~ aElement0(X1)
        | ~ aReductOfIn0(xv,X1,xR)
        | ~ aElement0(sK8(xu,xv)) )
    | ~ spl25_21 ),
    inference(subsumption_resolution,[],[f456,f158]) ).

tff(f456,plain,
    ( ! [X0: $i,X1: $i] :
        ( ~ aReductOfIn0(xu,X0,xR)
        | ~ aElement0(X0)
        | ~ aReductOfIn0(xv,X0,xR)
        | ~ aReductOfIn0(xu,X1,xR)
        | ~ aElement0(xu)
        | ~ aElement0(X1)
        | ~ aReductOfIn0(xv,X1,xR)
        | ~ aElement0(sK8(xu,xv)) )
    | ~ spl25_21 ),
    inference(subsumption_resolution,[],[f455,f341]) ).

tff(f455,plain,
    ( ! [X0: $i,X1: $i] :
        ( ~ aReductOfIn0(xu,X0,xR)
        | ~ aElement0(xv)
        | ~ aElement0(X0)
        | ~ aReductOfIn0(xv,X0,xR)
        | ~ aReductOfIn0(xu,X1,xR)
        | ~ aElement0(xu)
        | ~ aElement0(X1)
        | ~ aReductOfIn0(xv,X1,xR)
        | ~ aElement0(sK8(xu,xv)) )
    | ~ spl25_21 ),
    inference(resolution,[],[f445,f449]) ).

tff(f449,plain,
    ( ! [X0: $i,X1: $i] :
        ( sP4(sK8(X1,xv))
        | ~ aReductOfIn0(X1,X0,xR)
        | ~ aElement0(X1)
        | ~ aElement0(X0)
        | ~ aReductOfIn0(xv,X0,xR)
        | ~ aElement0(sK8(X1,xv)) )
    | ~ spl25_21 ),
    inference(subsumption_resolution,[],[f446,f341]) ).

tff(f446,plain,
    ! [X0: $i,X1: $i] :
      ( ~ aReductOfIn0(xv,X0,xR)
      | ~ aReductOfIn0(X1,X0,xR)
      | ~ aElement0(xv)
      | ~ aElement0(X1)
      | ~ aElement0(X0)
      | sP4(sK8(X1,xv))
      | ~ aElement0(sK8(X1,xv)) ),
    inference(resolution,[],[f119,f181]) ).

tff(f181,plain,
    ! [X0: $i] :
      ( ~ sdtmndtasgtdt0(xv,xR,X0)
      | sP4(X0)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f59]) ).

tff(f59,plain,
    ! [X0] :
      ( ( ~ sdtmndtasgtdt0(xv,xR,X0)
        & ~ sdtmndtplgtdt0(xv,xR,X0)
        & ! [X1] :
            ( ~ sdtmndtplgtdt0(X1,xR,X0)
            | ~ aReductOfIn0(X1,xv,xR)
            | ~ aElement0(X1) )
        & ~ aReductOfIn0(X0,xv,xR)
        & ( xv != X0 ) )
      | sP4(X0)
      | ~ aElement0(X0) ),
    inference(definition_folding,[],[f37,f58]) ).

tff(f58,plain,
    ! [X0] :
      ( ( ~ sdtmndtasgtdt0(xu,xR,X0)
        & ~ sdtmndtplgtdt0(xu,xR,X0)
        & ! [X2] :
            ( ~ sdtmndtplgtdt0(X2,xR,X0)
            | ~ aReductOfIn0(X2,xu,xR)
            | ~ aElement0(X2) )
        & ~ aReductOfIn0(X0,xu,xR)
        & ( xu != X0 ) )
      | ~ sP4(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).

tff(f37,plain,
    ! [X0] :
      ( ( ~ sdtmndtasgtdt0(xv,xR,X0)
        & ~ sdtmndtplgtdt0(xv,xR,X0)
        & ! [X1] :
            ( ~ sdtmndtplgtdt0(X1,xR,X0)
            | ~ aReductOfIn0(X1,xv,xR)
            | ~ aElement0(X1) )
        & ~ aReductOfIn0(X0,xv,xR)
        & ( xv != X0 ) )
      | ( ~ sdtmndtasgtdt0(xu,xR,X0)
        & ~ sdtmndtplgtdt0(xu,xR,X0)
        & ! [X2] :
            ( ~ sdtmndtplgtdt0(X2,xR,X0)
            | ~ aReductOfIn0(X2,xu,xR)
            | ~ aElement0(X2) )
        & ~ aReductOfIn0(X0,xu,xR)
        & ( xu != X0 ) )
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f27]) ).

tff(f27,plain,
    ~ ? [X0] :
        ( ( sdtmndtasgtdt0(xv,xR,X0)
          | sdtmndtplgtdt0(xv,xR,X0)
          | ? [X1] :
              ( sdtmndtplgtdt0(X1,xR,X0)
              & aReductOfIn0(X1,xv,xR)
              & aElement0(X1) )
          | aReductOfIn0(X0,xv,xR)
          | ( xv = X0 ) )
        & ( sdtmndtasgtdt0(xu,xR,X0)
          | sdtmndtplgtdt0(xu,xR,X0)
          | ? [X2] :
              ( sdtmndtplgtdt0(X2,xR,X0)
              & aReductOfIn0(X2,xu,xR)
              & aElement0(X2) )
          | aReductOfIn0(X0,xu,xR)
          | ( xu = X0 ) )
        & aElement0(X0) ),
    inference(rectify,[],[f23]) ).

tff(f23,negated_conjecture,
    ~ ? [X0] :
        ( ( sdtmndtasgtdt0(xv,xR,X0)
          | sdtmndtplgtdt0(xv,xR,X0)
          | ? [X1] :
              ( sdtmndtplgtdt0(X1,xR,X0)
              & aReductOfIn0(X1,xv,xR)
              & aElement0(X1) )
          | aReductOfIn0(X0,xv,xR)
          | ( xv = X0 ) )
        & ( sdtmndtasgtdt0(xu,xR,X0)
          | sdtmndtplgtdt0(xu,xR,X0)
          | ? [X1] :
              ( sdtmndtplgtdt0(X1,xR,X0)
              & aReductOfIn0(X1,xu,xR)
              & aElement0(X1) )
          | aReductOfIn0(X0,xu,xR)
          | ( xu = X0 ) )
        & aElement0(X0) ),
    inference(negated_conjecture,[],[f22]) ).

tff(f22,conjecture,
    ? [X0] :
      ( ( sdtmndtasgtdt0(xv,xR,X0)
        | sdtmndtplgtdt0(xv,xR,X0)
        | ? [X1] :
            ( sdtmndtplgtdt0(X1,xR,X0)
            & aReductOfIn0(X1,xv,xR)
            & aElement0(X1) )
        | aReductOfIn0(X0,xv,xR)
        | ( xv = X0 ) )
      & ( sdtmndtasgtdt0(xu,xR,X0)
        | sdtmndtplgtdt0(xu,xR,X0)
        | ? [X1] :
            ( sdtmndtplgtdt0(X1,xR,X0)
            & aReductOfIn0(X1,xu,xR)
            & aElement0(X1) )
        | aReductOfIn0(X0,xu,xR)
        | ( xu = X0 ) )
      & aElement0(X0) ),
    file('/export/starexec/sandbox/tmp/tmp.6DYLCjgnpJ/Vampire---4.8_25750',m__) ).

tff(f119,plain,
    ! [X3: $i,X4: $i,X5: $i] :
      ( sdtmndtasgtdt0(X5,xR,sK8(X4,X5))
      | ~ aReductOfIn0(X5,X3,xR)
      | ~ aReductOfIn0(X4,X3,xR)
      | ~ aElement0(X5)
      | ~ aElement0(X4)
      | ~ aElement0(X3) ),
    inference(cnf_transformation,[],[f69]) ).

tff(f445,plain,
    ! [X0: $i,X1: $i] :
      ( ~ sP4(sK8(xu,X0))
      | ~ aReductOfIn0(xu,X1,xR)
      | ~ aElement0(X0)
      | ~ aElement0(X1)
      | ~ aReductOfIn0(X0,X1,xR) ),
    inference(subsumption_resolution,[],[f442,f158]) ).

tff(f442,plain,
    ! [X0: $i,X1: $i] :
      ( ~ aReductOfIn0(X0,X1,xR)
      | ~ aReductOfIn0(xu,X1,xR)
      | ~ aElement0(X0)
      | ~ aElement0(xu)
      | ~ aElement0(X1)
      | ~ sP4(sK8(xu,X0)) ),
    inference(resolution,[],[f114,f176]) ).

tff(f176,plain,
    ! [X0: $i] :
      ( ~ sdtmndtasgtdt0(xu,xR,X0)
      | ~ sP4(X0) ),
    inference(cnf_transformation,[],[f89]) ).

tff(f89,plain,
    ! [X0] :
      ( ( ~ sdtmndtasgtdt0(xu,xR,X0)
        & ~ sdtmndtplgtdt0(xu,xR,X0)
        & ! [X1] :
            ( ~ sdtmndtplgtdt0(X1,xR,X0)
            | ~ aReductOfIn0(X1,xu,xR)
            | ~ aElement0(X1) )
        & ~ aReductOfIn0(X0,xu,xR)
        & ( xu != X0 ) )
      | ~ sP4(X0) ),
    inference(rectify,[],[f88]) ).

tff(f88,plain,
    ! [X0] :
      ( ( ~ sdtmndtasgtdt0(xu,xR,X0)
        & ~ sdtmndtplgtdt0(xu,xR,X0)
        & ! [X2] :
            ( ~ sdtmndtplgtdt0(X2,xR,X0)
            | ~ aReductOfIn0(X2,xu,xR)
            | ~ aElement0(X2) )
        & ~ aReductOfIn0(X0,xu,xR)
        & ( xu != X0 ) )
      | ~ sP4(X0) ),
    inference(nnf_transformation,[],[f58]) ).

tff(f114,plain,
    ! [X3: $i,X4: $i,X5: $i] :
      ( sdtmndtasgtdt0(X4,xR,sK8(X4,X5))
      | ~ aReductOfIn0(X5,X3,xR)
      | ~ aReductOfIn0(X4,X3,xR)
      | ~ aElement0(X5)
      | ~ aElement0(X4)
      | ~ aElement0(X3) ),
    inference(cnf_transformation,[],[f69]) ).

tff(f350,plain,
    spl25_21,
    inference(avatar_split_clause,[],[f165,f340]) ).

tff(f165,plain,
    aElement0(xv),
    inference(cnf_transformation,[],[f87]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : COM017+4 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.11  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.10/0.31  % Computer : n023.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit   : 300
% 0.10/0.31  % WCLimit    : 300
% 0.10/0.31  % DateTime   : Tue Apr 30 18:57:10 EDT 2024
% 0.16/0.31  % CPUTime    : 
% 0.16/0.31  This is a FOF_THM_RFO_SEQ problem
% 0.16/0.31  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.6DYLCjgnpJ/Vampire---4.8_25750
% 0.62/0.80  % (25864)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2995ds/33Mi)
% 0.62/0.80  % (25863)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2995ds/78Mi)
% 0.62/0.80  % (25865)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 (2995ds/34Mi)
% 0.62/0.80  % (25861)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 (2995ds/34Mi)
% 0.62/0.80  % (25866)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/45Mi)
% 0.62/0.80  % (25862)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 (2995ds/51Mi)
% 0.62/0.80  % (25867)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 (2995ds/83Mi)
% 0.62/0.80  % (25868)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 (2995ds/56Mi)
% 0.62/0.81  % (25861)First to succeed.
% 0.62/0.81  % (25861)Refutation found. Thanks to Tanya!
% 0.62/0.81  % SZS status Theorem for Vampire---4
% 0.62/0.81  % SZS output start Proof for Vampire---4
% See solution above
% 0.62/0.81  % (25861)------------------------------
% 0.62/0.81  % (25861)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.62/0.81  % (25861)Termination reason: Refutation
% 0.62/0.81  
% 0.62/0.81  % (25861)Memory used [KB]: 1211
% 0.62/0.81  % (25861)Time elapsed: 0.012 s
% 0.62/0.81  % (25861)Instructions burned: 19 (million)
% 0.62/0.81  % (25861)------------------------------
% 0.62/0.81  % (25861)------------------------------
% 0.62/0.81  % (25859)Success in time 0.495 s
% 0.62/0.81  % Vampire---4.8 exiting
%------------------------------------------------------------------------------