TSTP Solution File: COM013+4 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : COM013+4 : TPTP v8.2.0. 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 : Mon May 20 19:09:59 EDT 2024

% Result   : Theorem 0.56s 0.75s
% Output   : Refutation 0.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   64 (   4 unt;   0 def)
%            Number of atoms       :  504 (  28 equ)
%            Maximal formula atoms :   46 (   7 avg)
%            Number of connectives :  670 ( 230   ~; 220   |; 187   &)
%                                         (   8 <=>;  25  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   8 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   12 (  10 usr;   3 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-3 aty)
%            Number of variables   :  179 ( 129   !;  50   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f200,plain,
    $false,
    inference(avatar_sat_refutation,[],[f113,f114,f199]) ).

fof(f199,plain,
    ( ~ spl8_1
    | ~ spl8_2 ),
    inference(avatar_contradiction_clause,[],[f198]) ).

fof(f198,plain,
    ( $false
    | ~ spl8_1
    | ~ spl8_2 ),
    inference(subsumption_resolution,[],[f192,f140]) ).

fof(f140,plain,
    ( sdtmndtasgtdt0(sK1(sK0),xR,sK2(sK1(sK0)))
    | ~ spl8_1
    | ~ spl8_2 ),
    inference(unit_resulting_resolution,[],[f117,f124,f73]) ).

fof(f73,plain,
    ! [X4] :
      ( sdtmndtasgtdt0(X4,xR,sK2(X4))
      | ~ iLess0(X4,sK0)
      | ~ aElement0(X4) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f45,plain,
    ( ! [X1] :
        ( ~ aNormalFormOfIn0(X1,sK0,xR)
        & ( aReductOfIn0(sK1(X1),X1,xR)
          | ( ~ sdtmndtasgtdt0(sK0,xR,X1)
            & ~ sdtmndtplgtdt0(sK0,xR,X1)
            & ! [X3] :
                ( ~ sdtmndtplgtdt0(X3,xR,X1)
                | ~ aReductOfIn0(X3,sK0,xR)
                | ~ aElement0(X3) )
            & ~ aReductOfIn0(X1,sK0,xR)
            & sK0 != X1 )
          | ~ aElement0(X1) ) )
    & ! [X4] :
        ( ( aNormalFormOfIn0(sK2(X4),X4,xR)
          & ! [X6] : ~ aReductOfIn0(X6,sK2(X4),xR)
          & sdtmndtasgtdt0(X4,xR,sK2(X4))
          & ( ( sdtmndtplgtdt0(X4,xR,sK2(X4))
              & ( ( sdtmndtplgtdt0(sK3(X4),xR,sK2(X4))
                  & aReductOfIn0(sK3(X4),X4,xR)
                  & aElement0(sK3(X4)) )
                | aReductOfIn0(sK2(X4),X4,xR) ) )
            | sK2(X4) = X4 )
          & aElement0(sK2(X4)) )
        | ~ iLess0(X4,sK0)
        | ~ aElement0(X4) )
    & aElement0(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f40,f44,f43,f42,f41]) ).

fof(f41,plain,
    ( ? [X0] :
        ( ! [X1] :
            ( ~ aNormalFormOfIn0(X1,X0,xR)
            & ( ? [X2] : aReductOfIn0(X2,X1,xR)
              | ( ~ sdtmndtasgtdt0(X0,xR,X1)
                & ~ sdtmndtplgtdt0(X0,xR,X1)
                & ! [X3] :
                    ( ~ sdtmndtplgtdt0(X3,xR,X1)
                    | ~ aReductOfIn0(X3,X0,xR)
                    | ~ aElement0(X3) )
                & ~ aReductOfIn0(X1,X0,xR)
                & X0 != X1 )
              | ~ aElement0(X1) ) )
        & ! [X4] :
            ( ? [X5] :
                ( aNormalFormOfIn0(X5,X4,xR)
                & ! [X6] : ~ aReductOfIn0(X6,X5,xR)
                & sdtmndtasgtdt0(X4,xR,X5)
                & ( ( sdtmndtplgtdt0(X4,xR,X5)
                    & ( ? [X7] :
                          ( sdtmndtplgtdt0(X7,xR,X5)
                          & aReductOfIn0(X7,X4,xR)
                          & aElement0(X7) )
                      | aReductOfIn0(X5,X4,xR) ) )
                  | X4 = X5 )
                & aElement0(X5) )
            | ~ iLess0(X4,X0)
            | ~ aElement0(X4) )
        & aElement0(X0) )
   => ( ! [X1] :
          ( ~ aNormalFormOfIn0(X1,sK0,xR)
          & ( ? [X2] : aReductOfIn0(X2,X1,xR)
            | ( ~ sdtmndtasgtdt0(sK0,xR,X1)
              & ~ sdtmndtplgtdt0(sK0,xR,X1)
              & ! [X3] :
                  ( ~ sdtmndtplgtdt0(X3,xR,X1)
                  | ~ aReductOfIn0(X3,sK0,xR)
                  | ~ aElement0(X3) )
              & ~ aReductOfIn0(X1,sK0,xR)
              & sK0 != X1 )
            | ~ aElement0(X1) ) )
      & ! [X4] :
          ( ? [X5] :
              ( aNormalFormOfIn0(X5,X4,xR)
              & ! [X6] : ~ aReductOfIn0(X6,X5,xR)
              & sdtmndtasgtdt0(X4,xR,X5)
              & ( ( sdtmndtplgtdt0(X4,xR,X5)
                  & ( ? [X7] :
                        ( sdtmndtplgtdt0(X7,xR,X5)
                        & aReductOfIn0(X7,X4,xR)
                        & aElement0(X7) )
                    | aReductOfIn0(X5,X4,xR) ) )
                | X4 = X5 )
              & aElement0(X5) )
          | ~ iLess0(X4,sK0)
          | ~ aElement0(X4) )
      & aElement0(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f42,plain,
    ! [X1] :
      ( ? [X2] : aReductOfIn0(X2,X1,xR)
     => aReductOfIn0(sK1(X1),X1,xR) ),
    introduced(choice_axiom,[]) ).

fof(f43,plain,
    ! [X4] :
      ( ? [X5] :
          ( aNormalFormOfIn0(X5,X4,xR)
          & ! [X6] : ~ aReductOfIn0(X6,X5,xR)
          & sdtmndtasgtdt0(X4,xR,X5)
          & ( ( sdtmndtplgtdt0(X4,xR,X5)
              & ( ? [X7] :
                    ( sdtmndtplgtdt0(X7,xR,X5)
                    & aReductOfIn0(X7,X4,xR)
                    & aElement0(X7) )
                | aReductOfIn0(X5,X4,xR) ) )
            | X4 = X5 )
          & aElement0(X5) )
     => ( aNormalFormOfIn0(sK2(X4),X4,xR)
        & ! [X6] : ~ aReductOfIn0(X6,sK2(X4),xR)
        & sdtmndtasgtdt0(X4,xR,sK2(X4))
        & ( ( sdtmndtplgtdt0(X4,xR,sK2(X4))
            & ( ? [X7] :
                  ( sdtmndtplgtdt0(X7,xR,sK2(X4))
                  & aReductOfIn0(X7,X4,xR)
                  & aElement0(X7) )
              | aReductOfIn0(sK2(X4),X4,xR) ) )
          | sK2(X4) = X4 )
        & aElement0(sK2(X4)) ) ),
    introduced(choice_axiom,[]) ).

fof(f44,plain,
    ! [X4] :
      ( ? [X7] :
          ( sdtmndtplgtdt0(X7,xR,sK2(X4))
          & aReductOfIn0(X7,X4,xR)
          & aElement0(X7) )
     => ( sdtmndtplgtdt0(sK3(X4),xR,sK2(X4))
        & aReductOfIn0(sK3(X4),X4,xR)
        & aElement0(sK3(X4)) ) ),
    introduced(choice_axiom,[]) ).

fof(f40,plain,
    ? [X0] :
      ( ! [X1] :
          ( ~ aNormalFormOfIn0(X1,X0,xR)
          & ( ? [X2] : aReductOfIn0(X2,X1,xR)
            | ( ~ sdtmndtasgtdt0(X0,xR,X1)
              & ~ sdtmndtplgtdt0(X0,xR,X1)
              & ! [X3] :
                  ( ~ sdtmndtplgtdt0(X3,xR,X1)
                  | ~ aReductOfIn0(X3,X0,xR)
                  | ~ aElement0(X3) )
              & ~ aReductOfIn0(X1,X0,xR)
              & X0 != X1 )
            | ~ aElement0(X1) ) )
      & ! [X4] :
          ( ? [X5] :
              ( aNormalFormOfIn0(X5,X4,xR)
              & ! [X6] : ~ aReductOfIn0(X6,X5,xR)
              & sdtmndtasgtdt0(X4,xR,X5)
              & ( ( sdtmndtplgtdt0(X4,xR,X5)
                  & ( ? [X7] :
                        ( sdtmndtplgtdt0(X7,xR,X5)
                        & aReductOfIn0(X7,X4,xR)
                        & aElement0(X7) )
                    | aReductOfIn0(X5,X4,xR) ) )
                | X4 = X5 )
              & aElement0(X5) )
          | ~ iLess0(X4,X0)
          | ~ aElement0(X4) )
      & aElement0(X0) ),
    inference(rectify,[],[f25]) ).

fof(f25,plain,
    ? [X0] :
      ( ! [X5] :
          ( ~ aNormalFormOfIn0(X5,X0,xR)
          & ( ? [X6] : aReductOfIn0(X6,X5,xR)
            | ( ~ sdtmndtasgtdt0(X0,xR,X5)
              & ~ sdtmndtplgtdt0(X0,xR,X5)
              & ! [X7] :
                  ( ~ sdtmndtplgtdt0(X7,xR,X5)
                  | ~ aReductOfIn0(X7,X0,xR)
                  | ~ aElement0(X7) )
              & ~ aReductOfIn0(X5,X0,xR)
              & X0 != X5 )
            | ~ aElement0(X5) ) )
      & ! [X1] :
          ( ? [X2] :
              ( aNormalFormOfIn0(X2,X1,xR)
              & ! [X3] : ~ aReductOfIn0(X3,X2,xR)
              & sdtmndtasgtdt0(X1,xR,X2)
              & ( ( sdtmndtplgtdt0(X1,xR,X2)
                  & ( ? [X4] :
                        ( sdtmndtplgtdt0(X4,xR,X2)
                        & aReductOfIn0(X4,X1,xR)
                        & aElement0(X4) )
                    | aReductOfIn0(X2,X1,xR) ) )
                | X1 = X2 )
              & aElement0(X2) )
          | ~ iLess0(X1,X0)
          | ~ aElement0(X1) )
      & aElement0(X0) ),
    inference(flattening,[],[f24]) ).

fof(f24,plain,
    ? [X0] :
      ( ! [X5] :
          ( ~ aNormalFormOfIn0(X5,X0,xR)
          & ( ? [X6] : aReductOfIn0(X6,X5,xR)
            | ( ~ sdtmndtasgtdt0(X0,xR,X5)
              & ~ sdtmndtplgtdt0(X0,xR,X5)
              & ! [X7] :
                  ( ~ sdtmndtplgtdt0(X7,xR,X5)
                  | ~ aReductOfIn0(X7,X0,xR)
                  | ~ aElement0(X7) )
              & ~ aReductOfIn0(X5,X0,xR)
              & X0 != X5 )
            | ~ aElement0(X5) ) )
      & ! [X1] :
          ( ? [X2] :
              ( aNormalFormOfIn0(X2,X1,xR)
              & ! [X3] : ~ aReductOfIn0(X3,X2,xR)
              & sdtmndtasgtdt0(X1,xR,X2)
              & ( ( sdtmndtplgtdt0(X1,xR,X2)
                  & ( ? [X4] :
                        ( sdtmndtplgtdt0(X4,xR,X2)
                        & aReductOfIn0(X4,X1,xR)
                        & aElement0(X4) )
                    | aReductOfIn0(X2,X1,xR) ) )
                | X1 = X2 )
              & aElement0(X2) )
          | ~ iLess0(X1,X0)
          | ~ aElement0(X1) )
      & aElement0(X0) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f17,plain,
    ~ ! [X0] :
        ( aElement0(X0)
       => ( ! [X1] :
              ( aElement0(X1)
             => ( iLess0(X1,X0)
               => ? [X2] :
                    ( aNormalFormOfIn0(X2,X1,xR)
                    & ~ ? [X3] : aReductOfIn0(X3,X2,xR)
                    & sdtmndtasgtdt0(X1,xR,X2)
                    & ( ( sdtmndtplgtdt0(X1,xR,X2)
                        & ( ? [X4] :
                              ( sdtmndtplgtdt0(X4,xR,X2)
                              & aReductOfIn0(X4,X1,xR)
                              & aElement0(X4) )
                          | aReductOfIn0(X2,X1,xR) ) )
                      | X1 = X2 )
                    & aElement0(X2) ) ) )
         => ? [X5] :
              ( aNormalFormOfIn0(X5,X0,xR)
              | ( ~ ? [X6] : aReductOfIn0(X6,X5,xR)
                & ( sdtmndtasgtdt0(X0,xR,X5)
                  | sdtmndtplgtdt0(X0,xR,X5)
                  | ? [X7] :
                      ( sdtmndtplgtdt0(X7,xR,X5)
                      & aReductOfIn0(X7,X0,xR)
                      & aElement0(X7) )
                  | aReductOfIn0(X5,X0,xR)
                  | X0 = X5 )
                & aElement0(X5) ) ) ) ),
    inference(rectify,[],[f16]) ).

fof(f16,negated_conjecture,
    ~ ! [X0] :
        ( aElement0(X0)
       => ( ! [X1] :
              ( aElement0(X1)
             => ( iLess0(X1,X0)
               => ? [X2] :
                    ( aNormalFormOfIn0(X2,X1,xR)
                    & ~ ? [X3] : aReductOfIn0(X3,X2,xR)
                    & sdtmndtasgtdt0(X1,xR,X2)
                    & ( ( sdtmndtplgtdt0(X1,xR,X2)
                        & ( ? [X3] :
                              ( sdtmndtplgtdt0(X3,xR,X2)
                              & aReductOfIn0(X3,X1,xR)
                              & aElement0(X3) )
                          | aReductOfIn0(X2,X1,xR) ) )
                      | X1 = X2 )
                    & aElement0(X2) ) ) )
         => ? [X1] :
              ( aNormalFormOfIn0(X1,X0,xR)
              | ( ~ ? [X2] : aReductOfIn0(X2,X1,xR)
                & ( sdtmndtasgtdt0(X0,xR,X1)
                  | sdtmndtplgtdt0(X0,xR,X1)
                  | ? [X2] :
                      ( sdtmndtplgtdt0(X2,xR,X1)
                      & aReductOfIn0(X2,X0,xR)
                      & aElement0(X2) )
                  | aReductOfIn0(X1,X0,xR)
                  | X0 = X1 )
                & aElement0(X1) ) ) ) ),
    inference(negated_conjecture,[],[f15]) ).

fof(f15,conjecture,
    ! [X0] :
      ( aElement0(X0)
     => ( ! [X1] :
            ( aElement0(X1)
           => ( iLess0(X1,X0)
             => ? [X2] :
                  ( aNormalFormOfIn0(X2,X1,xR)
                  & ~ ? [X3] : aReductOfIn0(X3,X2,xR)
                  & sdtmndtasgtdt0(X1,xR,X2)
                  & ( ( sdtmndtplgtdt0(X1,xR,X2)
                      & ( ? [X3] :
                            ( sdtmndtplgtdt0(X3,xR,X2)
                            & aReductOfIn0(X3,X1,xR)
                            & aElement0(X3) )
                        | aReductOfIn0(X2,X1,xR) ) )
                    | X1 = X2 )
                  & aElement0(X2) ) ) )
       => ? [X1] :
            ( aNormalFormOfIn0(X1,X0,xR)
            | ( ~ ? [X2] : aReductOfIn0(X2,X1,xR)
              & ( sdtmndtasgtdt0(X0,xR,X1)
                | sdtmndtplgtdt0(X0,xR,X1)
                | ? [X2] :
                    ( sdtmndtplgtdt0(X2,xR,X1)
                    & aReductOfIn0(X2,X0,xR)
                    & aElement0(X2) )
                | aReductOfIn0(X1,X0,xR)
                | X0 = X1 )
              & aElement0(X1) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(f124,plain,
    ( iLess0(sK1(sK0),sK0)
    | ~ spl8_1
    | ~ spl8_2 ),
    inference(unit_resulting_resolution,[],[f107,f117,f112,f63]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( iLess0(X1,X0)
      | ~ aReductOfIn0(X1,X0,xR)
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,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) )
    & aRewritingSystem0(xR) ),
    inference(flattening,[],[f22]) ).

fof(f22,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) )
    & aRewritingSystem0(xR) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,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) ) )
    & aRewritingSystem0(xR) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__587) ).

fof(f112,plain,
    ( aReductOfIn0(sK1(sK0),sK0,xR)
    | ~ spl8_2 ),
    inference(avatar_component_clause,[],[f110]) ).

fof(f110,plain,
    ( spl8_2
  <=> aReductOfIn0(sK1(sK0),sK0,xR) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).

fof(f107,plain,
    ( aElement0(sK0)
    | ~ spl8_1 ),
    inference(avatar_component_clause,[],[f106]) ).

fof(f106,plain,
    ( spl8_1
  <=> aElement0(sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).

fof(f117,plain,
    ( aElement0(sK1(sK0))
    | ~ spl8_1
    | ~ spl8_2 ),
    inference(unit_resulting_resolution,[],[f107,f62,f112,f87]) ).

fof(f87,plain,
    ! [X2,X0,X1] :
      ( aElement0(X2)
      | ~ aReductOfIn0(X2,X0,X1)
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( aElement0(X2)
          | ~ aReductOfIn0(X2,X0,X1) )
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(flattening,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( aElement0(X2)
          | ~ aReductOfIn0(X2,X0,X1) )
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( ( aRewritingSystem0(X1)
        & aElement0(X0) )
     => ! [X2] :
          ( aReductOfIn0(X2,X0,X1)
         => aElement0(X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mReduct) ).

fof(f62,plain,
    aRewritingSystem0(xR),
    inference(cnf_transformation,[],[f23]) ).

fof(f192,plain,
    ( ~ sdtmndtasgtdt0(sK1(sK0),xR,sK2(sK1(sK0)))
    | ~ spl8_1
    | ~ spl8_2 ),
    inference(unit_resulting_resolution,[],[f107,f141,f166,f117,f161,f62,f97]) ).

fof(f97,plain,
    ! [X2,X3,X0,X1] :
      ( ~ aRewritingSystem0(X1)
      | ~ sdtmndtasgtdt0(X2,X1,X3)
      | ~ sdtmndtasgtdt0(X0,X1,X2)
      | ~ aElement0(X3)
      | ~ aElement0(X2)
      | sdtmndtasgtdt0(X0,X1,X3)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0,X1,X2,X3] :
      ( sdtmndtasgtdt0(X0,X1,X3)
      | ~ sdtmndtasgtdt0(X2,X1,X3)
      | ~ sdtmndtasgtdt0(X0,X1,X2)
      | ~ aElement0(X3)
      | ~ aElement0(X2)
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(flattening,[],[f36]) ).

fof(f36,plain,
    ! [X0,X1,X2,X3] :
      ( sdtmndtasgtdt0(X0,X1,X3)
      | ~ sdtmndtasgtdt0(X2,X1,X3)
      | ~ sdtmndtasgtdt0(X0,X1,X2)
      | ~ aElement0(X3)
      | ~ aElement0(X2)
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1,X2,X3] :
      ( ( aElement0(X3)
        & aElement0(X2)
        & aRewritingSystem0(X1)
        & aElement0(X0) )
     => ( ( sdtmndtasgtdt0(X2,X1,X3)
          & sdtmndtasgtdt0(X0,X1,X2) )
       => sdtmndtasgtdt0(X0,X1,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTCRTrans) ).

fof(f161,plain,
    ( sdtmndtasgtdt0(sK0,xR,sK1(sK0))
    | ~ spl8_1
    | ~ spl8_2 ),
    inference(unit_resulting_resolution,[],[f107,f62,f117,f154,f96]) ).

fof(f96,plain,
    ! [X2,X0,X1] :
      ( sdtmndtasgtdt0(X0,X1,X2)
      | ~ sdtmndtplgtdt0(X0,X1,X2)
      | ~ aElement0(X2)
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X0,X1,X2] :
      ( ( ( sdtmndtasgtdt0(X0,X1,X2)
          | ( ~ sdtmndtplgtdt0(X0,X1,X2)
            & X0 != X2 ) )
        & ( sdtmndtplgtdt0(X0,X1,X2)
          | X0 = X2
          | ~ sdtmndtasgtdt0(X0,X1,X2) ) )
      | ~ aElement0(X2)
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(flattening,[],[f55]) ).

fof(f55,plain,
    ! [X0,X1,X2] :
      ( ( ( sdtmndtasgtdt0(X0,X1,X2)
          | ( ~ sdtmndtplgtdt0(X0,X1,X2)
            & X0 != X2 ) )
        & ( sdtmndtplgtdt0(X0,X1,X2)
          | X0 = X2
          | ~ sdtmndtasgtdt0(X0,X1,X2) ) )
      | ~ aElement0(X2)
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(nnf_transformation,[],[f35]) ).

fof(f35,plain,
    ! [X0,X1,X2] :
      ( ( sdtmndtasgtdt0(X0,X1,X2)
      <=> ( sdtmndtplgtdt0(X0,X1,X2)
          | X0 = X2 ) )
      | ~ aElement0(X2)
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(flattening,[],[f34]) ).

fof(f34,plain,
    ! [X0,X1,X2] :
      ( ( sdtmndtasgtdt0(X0,X1,X2)
      <=> ( sdtmndtplgtdt0(X0,X1,X2)
          | X0 = X2 ) )
      | ~ aElement0(X2)
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0,X1,X2] :
      ( ( aElement0(X2)
        & aRewritingSystem0(X1)
        & aElement0(X0) )
     => ( sdtmndtasgtdt0(X0,X1,X2)
      <=> ( sdtmndtplgtdt0(X0,X1,X2)
          | X0 = X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTCRDef) ).

fof(f154,plain,
    ( sdtmndtplgtdt0(sK0,xR,sK1(sK0))
    | ~ spl8_1
    | ~ spl8_2 ),
    inference(unit_resulting_resolution,[],[f107,f117,f112,f62,f85]) ).

fof(f85,plain,
    ! [X2,X0,X1] :
      ( ~ aRewritingSystem0(X1)
      | ~ aReductOfIn0(X2,X0,X1)
      | ~ aElement0(X2)
      | sdtmndtplgtdt0(X0,X1,X2)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f50]) ).

fof(f50,plain,
    ! [X0,X1,X2] :
      ( ( ( sdtmndtplgtdt0(X0,X1,X2)
          | ( ! [X3] :
                ( ~ sdtmndtplgtdt0(X3,X1,X2)
                | ~ aReductOfIn0(X3,X0,X1)
                | ~ aElement0(X3) )
            & ~ aReductOfIn0(X2,X0,X1) ) )
        & ( ( sdtmndtplgtdt0(sK4(X0,X1,X2),X1,X2)
            & aReductOfIn0(sK4(X0,X1,X2),X0,X1)
            & aElement0(sK4(X0,X1,X2)) )
          | aReductOfIn0(X2,X0,X1)
          | ~ sdtmndtplgtdt0(X0,X1,X2) ) )
      | ~ aElement0(X2)
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f48,f49]) ).

fof(f49,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( sdtmndtplgtdt0(X4,X1,X2)
          & aReductOfIn0(X4,X0,X1)
          & aElement0(X4) )
     => ( sdtmndtplgtdt0(sK4(X0,X1,X2),X1,X2)
        & aReductOfIn0(sK4(X0,X1,X2),X0,X1)
        & aElement0(sK4(X0,X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f48,plain,
    ! [X0,X1,X2] :
      ( ( ( sdtmndtplgtdt0(X0,X1,X2)
          | ( ! [X3] :
                ( ~ sdtmndtplgtdt0(X3,X1,X2)
                | ~ aReductOfIn0(X3,X0,X1)
                | ~ aElement0(X3) )
            & ~ aReductOfIn0(X2,X0,X1) ) )
        & ( ? [X4] :
              ( sdtmndtplgtdt0(X4,X1,X2)
              & aReductOfIn0(X4,X0,X1)
              & aElement0(X4) )
          | aReductOfIn0(X2,X0,X1)
          | ~ sdtmndtplgtdt0(X0,X1,X2) ) )
      | ~ aElement0(X2)
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(rectify,[],[f47]) ).

fof(f47,plain,
    ! [X0,X1,X2] :
      ( ( ( sdtmndtplgtdt0(X0,X1,X2)
          | ( ! [X3] :
                ( ~ sdtmndtplgtdt0(X3,X1,X2)
                | ~ aReductOfIn0(X3,X0,X1)
                | ~ aElement0(X3) )
            & ~ aReductOfIn0(X2,X0,X1) ) )
        & ( ? [X3] :
              ( sdtmndtplgtdt0(X3,X1,X2)
              & aReductOfIn0(X3,X0,X1)
              & aElement0(X3) )
          | aReductOfIn0(X2,X0,X1)
          | ~ sdtmndtplgtdt0(X0,X1,X2) ) )
      | ~ aElement0(X2)
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(flattening,[],[f46]) ).

fof(f46,plain,
    ! [X0,X1,X2] :
      ( ( ( sdtmndtplgtdt0(X0,X1,X2)
          | ( ! [X3] :
                ( ~ sdtmndtplgtdt0(X3,X1,X2)
                | ~ aReductOfIn0(X3,X0,X1)
                | ~ aElement0(X3) )
            & ~ aReductOfIn0(X2,X0,X1) ) )
        & ( ? [X3] :
              ( sdtmndtplgtdt0(X3,X1,X2)
              & aReductOfIn0(X3,X0,X1)
              & aElement0(X3) )
          | aReductOfIn0(X2,X0,X1)
          | ~ sdtmndtplgtdt0(X0,X1,X2) ) )
      | ~ aElement0(X2)
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(nnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( ( sdtmndtplgtdt0(X0,X1,X2)
      <=> ( ? [X3] :
              ( sdtmndtplgtdt0(X3,X1,X2)
              & aReductOfIn0(X3,X0,X1)
              & aElement0(X3) )
          | aReductOfIn0(X2,X0,X1) ) )
      | ~ aElement0(X2)
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(flattening,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1,X2] :
      ( ( sdtmndtplgtdt0(X0,X1,X2)
      <=> ( ? [X3] :
              ( sdtmndtplgtdt0(X3,X1,X2)
              & aReductOfIn0(X3,X0,X1)
              & aElement0(X3) )
          | aReductOfIn0(X2,X0,X1) ) )
      | ~ aElement0(X2)
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1,X2] :
      ( ( aElement0(X2)
        & aRewritingSystem0(X1)
        & aElement0(X0) )
     => ( sdtmndtplgtdt0(X0,X1,X2)
      <=> ( ? [X3] :
              ( sdtmndtplgtdt0(X3,X1,X2)
              & aReductOfIn0(X3,X0,X1)
              & aElement0(X3) )
          | aReductOfIn0(X2,X0,X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTCDef) ).

fof(f166,plain,
    ( ~ sdtmndtasgtdt0(sK0,xR,sK2(sK1(sK0)))
    | ~ spl8_1
    | ~ spl8_2 ),
    inference(unit_resulting_resolution,[],[f141,f139,f80]) ).

fof(f80,plain,
    ! [X1] :
      ( aReductOfIn0(sK1(X1),X1,xR)
      | ~ sdtmndtasgtdt0(sK0,xR,X1)
      | ~ aElement0(X1) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f139,plain,
    ( ! [X0] : ~ aReductOfIn0(X0,sK2(sK1(sK0)),xR)
    | ~ spl8_1
    | ~ spl8_2 ),
    inference(unit_resulting_resolution,[],[f117,f124,f74]) ).

fof(f74,plain,
    ! [X6,X4] :
      ( ~ iLess0(X4,sK0)
      | ~ aReductOfIn0(X6,sK2(X4),xR)
      | ~ aElement0(X4) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f141,plain,
    ( aElement0(sK2(sK1(sK0)))
    | ~ spl8_1
    | ~ spl8_2 ),
    inference(unit_resulting_resolution,[],[f117,f124,f68]) ).

fof(f68,plain,
    ! [X4] :
      ( aElement0(sK2(X4))
      | ~ iLess0(X4,sK0)
      | ~ aElement0(X4) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f114,plain,
    spl8_1,
    inference(avatar_split_clause,[],[f67,f106]) ).

fof(f67,plain,
    aElement0(sK0),
    inference(cnf_transformation,[],[f45]) ).

fof(f113,plain,
    ( ~ spl8_1
    | spl8_2 ),
    inference(avatar_split_clause,[],[f102,f110,f106]) ).

fof(f102,plain,
    ( aReductOfIn0(sK1(sK0),sK0,xR)
    | ~ aElement0(sK0) ),
    inference(equality_resolution,[],[f76]) ).

fof(f76,plain,
    ! [X1] :
      ( aReductOfIn0(sK1(X1),X1,xR)
      | sK0 != X1
      | ~ aElement0(X1) ),
    inference(cnf_transformation,[],[f45]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : COM013+4 : TPTP v8.2.0. Released v4.0.0.
% 0.13/0.14  % 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
% 0.14/0.35  % Computer : n023.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 10:09:38 EDT 2024
% 0.21/0.35  % CPUTime    : 
% 0.21/0.35  This is a FOF_THM_RFO_SEQ problem
% 0.21/0.35  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/benchmark/theBenchmark.p
% 0.56/0.74  % (3150)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on theBenchmark for (2996ds/56Mi)
% 0.56/0.74  % (3143)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 theBenchmark for (2996ds/34Mi)
% 0.56/0.74  % (3145)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on theBenchmark for (2996ds/78Mi)
% 0.56/0.74  % (3144)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 theBenchmark for (2996ds/51Mi)
% 0.56/0.74  % (3148)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on theBenchmark for (2996ds/45Mi)
% 0.56/0.74  % (3146)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on theBenchmark for (2996ds/33Mi)
% 0.56/0.74  % (3147)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 theBenchmark for (2996ds/34Mi)
% 0.56/0.74  % (3149)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 theBenchmark for (2996ds/83Mi)
% 0.56/0.74  % (3146)First to succeed.
% 0.56/0.74  % (3144)Also succeeded, but the first one will report.
% 0.56/0.75  % (3145)Also succeeded, but the first one will report.
% 0.56/0.75  % (3150)Also succeeded, but the first one will report.
% 0.56/0.75  % (3146)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3010"
% 0.56/0.75  % (3146)Refutation found. Thanks to Tanya!
% 0.56/0.75  % SZS status Theorem for theBenchmark
% 0.56/0.75  % SZS output start Proof for theBenchmark
% See solution above
% 0.56/0.75  % (3146)------------------------------
% 0.56/0.75  % (3146)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.75  % (3146)Termination reason: Refutation
% 0.56/0.75  
% 0.56/0.75  % (3146)Memory used [KB]: 1142
% 0.56/0.75  % (3146)Time elapsed: 0.009 s
% 0.56/0.75  % (3146)Instructions burned: 13 (million)
% 0.56/0.75  % (3010)Success in time 0.383 s
% 0.56/0.75  % Vampire---4.8 exiting
%------------------------------------------------------------------------------