TSTP Solution File: SEU221+3 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEU221+3 : TPTP v8.1.2. Released v3.2.0.
% 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 : 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 09:21:10 EDT 2024

% Result   : Theorem 0.60s 0.76s
% Output   : Refutation 0.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   29
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   93 (   8 unt;   0 def)
%            Number of atoms       :  474 ( 114 equ)
%            Maximal formula atoms :   19 (   5 avg)
%            Number of connectives :  647 ( 266   ~; 257   |;  95   &)
%                                         (  12 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   5 prp; 0-4 aty)
%            Number of functors    :   10 (  10 usr;   1 con; 0-2 aty)
%            Number of variables   :   99 (  82   !;  17   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f513,plain,
    $false,
    inference(avatar_sat_refutation,[],[f247,f252,f258,f264,f512]) ).

fof(f512,plain,
    ( ~ spl14_1
    | ~ spl14_2
    | ~ spl14_3
    | ~ spl14_4 ),
    inference(avatar_contradiction_clause,[],[f511]) ).

fof(f511,plain,
    ( $false
    | ~ spl14_1
    | ~ spl14_2
    | ~ spl14_3
    | ~ spl14_4 ),
    inference(subsumption_resolution,[],[f510,f237]) ).

fof(f237,plain,
    ( relation(function_inverse(sK1))
    | ~ spl14_1 ),
    inference(avatar_component_clause,[],[f236]) ).

fof(f236,plain,
    ( spl14_1
  <=> relation(function_inverse(sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl14_1])]) ).

fof(f510,plain,
    ( ~ relation(function_inverse(sK1))
    | ~ spl14_1
    | ~ spl14_2
    | ~ spl14_3
    | ~ spl14_4 ),
    inference(subsumption_resolution,[],[f509,f241]) ).

fof(f241,plain,
    ( function(function_inverse(sK1))
    | ~ spl14_2 ),
    inference(avatar_component_clause,[],[f240]) ).

fof(f240,plain,
    ( spl14_2
  <=> function(function_inverse(sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl14_2])]) ).

fof(f509,plain,
    ( ~ function(function_inverse(sK1))
    | ~ relation(function_inverse(sK1))
    | ~ spl14_1
    | ~ spl14_2
    | ~ spl14_3
    | ~ spl14_4 ),
    inference(subsumption_resolution,[],[f508,f112]) ).

fof(f112,plain,
    ~ one_to_one(function_inverse(sK1)),
    inference(cnf_transformation,[],[f80]) ).

fof(f80,plain,
    ( ~ one_to_one(function_inverse(sK1))
    & one_to_one(sK1)
    & function(sK1)
    & relation(sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f46,f79]) ).

fof(f79,plain,
    ( ? [X0] :
        ( ~ one_to_one(function_inverse(X0))
        & one_to_one(X0)
        & function(X0)
        & relation(X0) )
   => ( ~ one_to_one(function_inverse(sK1))
      & one_to_one(sK1)
      & function(sK1)
      & relation(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f46,plain,
    ? [X0] :
      ( ~ one_to_one(function_inverse(X0))
      & one_to_one(X0)
      & function(X0)
      & relation(X0) ),
    inference(flattening,[],[f45]) ).

fof(f45,plain,
    ? [X0] :
      ( ~ one_to_one(function_inverse(X0))
      & one_to_one(X0)
      & function(X0)
      & relation(X0) ),
    inference(ennf_transformation,[],[f39]) ).

fof(f39,negated_conjecture,
    ~ ! [X0] :
        ( ( function(X0)
          & relation(X0) )
       => ( one_to_one(X0)
         => one_to_one(function_inverse(X0)) ) ),
    inference(negated_conjecture,[],[f38]) ).

fof(f38,conjecture,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ( one_to_one(X0)
       => one_to_one(function_inverse(X0)) ) ),
    file('/export/starexec/sandbox/tmp/tmp.HQgwq86rBI/Vampire---4.8_20521',t62_funct_1) ).

fof(f508,plain,
    ( one_to_one(function_inverse(sK1))
    | ~ function(function_inverse(sK1))
    | ~ relation(function_inverse(sK1))
    | ~ spl14_1
    | ~ spl14_2
    | ~ spl14_3
    | ~ spl14_4 ),
    inference(trivial_inequality_removal,[],[f507]) ).

fof(f507,plain,
    ( sK9(function_inverse(sK1)) != sK9(function_inverse(sK1))
    | one_to_one(function_inverse(sK1))
    | ~ function(function_inverse(sK1))
    | ~ relation(function_inverse(sK1))
    | ~ spl14_1
    | ~ spl14_2
    | ~ spl14_3
    | ~ spl14_4 ),
    inference(superposition,[],[f147,f464]) ).

fof(f464,plain,
    ( sK9(function_inverse(sK1)) = sK10(function_inverse(sK1))
    | ~ spl14_1
    | ~ spl14_2
    | ~ spl14_3
    | ~ spl14_4 ),
    inference(backward_demodulation,[],[f450,f463]) ).

fof(f463,plain,
    ( sK9(function_inverse(sK1)) = apply(sK1,apply(function_inverse(sK1),sK9(function_inverse(sK1))))
    | ~ spl14_3 ),
    inference(subsumption_resolution,[],[f462,f109]) ).

fof(f109,plain,
    relation(sK1),
    inference(cnf_transformation,[],[f80]) ).

fof(f462,plain,
    ( sK9(function_inverse(sK1)) = apply(sK1,apply(function_inverse(sK1),sK9(function_inverse(sK1))))
    | ~ relation(sK1)
    | ~ spl14_3 ),
    inference(subsumption_resolution,[],[f461,f110]) ).

fof(f110,plain,
    function(sK1),
    inference(cnf_transformation,[],[f80]) ).

fof(f461,plain,
    ( sK9(function_inverse(sK1)) = apply(sK1,apply(function_inverse(sK1),sK9(function_inverse(sK1))))
    | ~ function(sK1)
    | ~ relation(sK1)
    | ~ spl14_3 ),
    inference(subsumption_resolution,[],[f453,f111]) ).

fof(f111,plain,
    one_to_one(sK1),
    inference(cnf_transformation,[],[f80]) ).

fof(f453,plain,
    ( sK9(function_inverse(sK1)) = apply(sK1,apply(function_inverse(sK1),sK9(function_inverse(sK1))))
    | ~ one_to_one(sK1)
    | ~ function(sK1)
    | ~ relation(sK1)
    | ~ spl14_3 ),
    inference(resolution,[],[f430,f113]) ).

fof(f113,plain,
    ! [X0,X1] :
      ( ~ in(X0,relation_rng(X1))
      | apply(X1,apply(function_inverse(X1),X0)) = X0
      | ~ one_to_one(X1)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f48]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( ( apply(relation_composition(function_inverse(X1),X1),X0) = X0
        & apply(X1,apply(function_inverse(X1),X0)) = X0 )
      | ~ in(X0,relation_rng(X1))
      | ~ one_to_one(X1)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(flattening,[],[f47]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( ( apply(relation_composition(function_inverse(X1),X1),X0) = X0
        & apply(X1,apply(function_inverse(X1),X0)) = X0 )
      | ~ in(X0,relation_rng(X1))
      | ~ one_to_one(X1)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(ennf_transformation,[],[f36]) ).

fof(f36,axiom,
    ! [X0,X1] :
      ( ( function(X1)
        & relation(X1) )
     => ( ( in(X0,relation_rng(X1))
          & one_to_one(X1) )
       => ( apply(relation_composition(function_inverse(X1),X1),X0) = X0
          & apply(X1,apply(function_inverse(X1),X0)) = X0 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.HQgwq86rBI/Vampire---4.8_20521',t57_funct_1) ).

fof(f430,plain,
    ( in(sK9(function_inverse(sK1)),relation_rng(sK1))
    | ~ spl14_3 ),
    inference(backward_demodulation,[],[f246,f425]) ).

fof(f425,plain,
    relation_dom(function_inverse(sK1)) = relation_rng(sK1),
    inference(subsumption_resolution,[],[f424,f109]) ).

fof(f424,plain,
    ( relation_dom(function_inverse(sK1)) = relation_rng(sK1)
    | ~ relation(sK1) ),
    inference(subsumption_resolution,[],[f415,f110]) ).

fof(f415,plain,
    ( relation_dom(function_inverse(sK1)) = relation_rng(sK1)
    | ~ function(sK1)
    | ~ relation(sK1) ),
    inference(resolution,[],[f306,f111]) ).

fof(f306,plain,
    ! [X0] :
      ( ~ one_to_one(X0)
      | relation_rng(X0) = relation_dom(function_inverse(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(subsumption_resolution,[],[f305,f128]) ).

fof(f128,plain,
    ! [X0] :
      ( function(function_inverse(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f52]) ).

fof(f52,plain,
    ! [X0] :
      ( ( function(function_inverse(X0))
        & relation(function_inverse(X0)) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f51]) ).

fof(f51,plain,
    ! [X0] :
      ( ( function(function_inverse(X0))
        & relation(function_inverse(X0)) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ( function(function_inverse(X0))
        & relation(function_inverse(X0)) ) ),
    file('/export/starexec/sandbox/tmp/tmp.HQgwq86rBI/Vampire---4.8_20521',dt_k2_funct_1) ).

fof(f305,plain,
    ! [X0] :
      ( ~ function(function_inverse(X0))
      | relation_rng(X0) = relation_dom(function_inverse(X0))
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(duplicate_literal_removal,[],[f302]) ).

fof(f302,plain,
    ! [X0] :
      ( ~ function(function_inverse(X0))
      | relation_rng(X0) = relation_dom(function_inverse(X0))
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(resolution,[],[f184,f127]) ).

fof(f127,plain,
    ! [X0] :
      ( relation(function_inverse(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f52]) ).

fof(f184,plain,
    ! [X0] :
      ( ~ relation(function_inverse(X0))
      | ~ function(function_inverse(X0))
      | relation_rng(X0) = relation_dom(function_inverse(X0))
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f120]) ).

fof(f120,plain,
    ! [X0,X1] :
      ( relation_rng(X0) = relation_dom(X1)
      | function_inverse(X0) != X1
      | ~ function(X1)
      | ~ relation(X1)
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f88,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( function_inverse(X0) = X1
              | ( ( sK3(X0,X1) != apply(X1,sK2(X0,X1))
                  | ~ in(sK2(X0,X1),relation_rng(X0)) )
                & sK2(X0,X1) = apply(X0,sK3(X0,X1))
                & in(sK3(X0,X1),relation_dom(X0)) )
              | ~ sP0(sK2(X0,X1),sK3(X0,X1),X0,X1)
              | relation_rng(X0) != relation_dom(X1) )
            & ( ( ! [X4,X5] :
                    ( ( ( apply(X1,X4) = X5
                        & in(X4,relation_rng(X0)) )
                      | apply(X0,X5) != X4
                      | ~ in(X5,relation_dom(X0)) )
                    & sP0(X4,X5,X0,X1) )
                & relation_rng(X0) = relation_dom(X1) )
              | function_inverse(X0) != X1 ) )
          | ~ function(X1)
          | ~ relation(X1) )
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f86,f87]) ).

fof(f87,plain,
    ! [X0,X1] :
      ( ? [X2,X3] :
          ( ( ( apply(X1,X2) != X3
              | ~ in(X2,relation_rng(X0)) )
            & apply(X0,X3) = X2
            & in(X3,relation_dom(X0)) )
          | ~ sP0(X2,X3,X0,X1) )
     => ( ( ( sK3(X0,X1) != apply(X1,sK2(X0,X1))
            | ~ in(sK2(X0,X1),relation_rng(X0)) )
          & sK2(X0,X1) = apply(X0,sK3(X0,X1))
          & in(sK3(X0,X1),relation_dom(X0)) )
        | ~ sP0(sK2(X0,X1),sK3(X0,X1),X0,X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f86,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( function_inverse(X0) = X1
              | ? [X2,X3] :
                  ( ( ( apply(X1,X2) != X3
                      | ~ in(X2,relation_rng(X0)) )
                    & apply(X0,X3) = X2
                    & in(X3,relation_dom(X0)) )
                  | ~ sP0(X2,X3,X0,X1) )
              | relation_rng(X0) != relation_dom(X1) )
            & ( ( ! [X4,X5] :
                    ( ( ( apply(X1,X4) = X5
                        & in(X4,relation_rng(X0)) )
                      | apply(X0,X5) != X4
                      | ~ in(X5,relation_dom(X0)) )
                    & sP0(X4,X5,X0,X1) )
                & relation_rng(X0) = relation_dom(X1) )
              | function_inverse(X0) != X1 ) )
          | ~ function(X1)
          | ~ relation(X1) )
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(rectify,[],[f85]) ).

fof(f85,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( function_inverse(X0) = X1
              | ? [X2,X3] :
                  ( ( ( apply(X1,X2) != X3
                      | ~ in(X2,relation_rng(X0)) )
                    & apply(X0,X3) = X2
                    & in(X3,relation_dom(X0)) )
                  | ~ sP0(X2,X3,X0,X1) )
              | relation_rng(X0) != relation_dom(X1) )
            & ( ( ! [X2,X3] :
                    ( ( ( apply(X1,X2) = X3
                        & in(X2,relation_rng(X0)) )
                      | apply(X0,X3) != X2
                      | ~ in(X3,relation_dom(X0)) )
                    & sP0(X2,X3,X0,X1) )
                & relation_rng(X0) = relation_dom(X1) )
              | function_inverse(X0) != X1 ) )
          | ~ function(X1)
          | ~ relation(X1) )
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f84]) ).

fof(f84,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( function_inverse(X0) = X1
              | ? [X2,X3] :
                  ( ( ( apply(X1,X2) != X3
                      | ~ in(X2,relation_rng(X0)) )
                    & apply(X0,X3) = X2
                    & in(X3,relation_dom(X0)) )
                  | ~ sP0(X2,X3,X0,X1) )
              | relation_rng(X0) != relation_dom(X1) )
            & ( ( ! [X2,X3] :
                    ( ( ( apply(X1,X2) = X3
                        & in(X2,relation_rng(X0)) )
                      | apply(X0,X3) != X2
                      | ~ in(X3,relation_dom(X0)) )
                    & sP0(X2,X3,X0,X1) )
                & relation_rng(X0) = relation_dom(X1) )
              | function_inverse(X0) != X1 ) )
          | ~ function(X1)
          | ~ relation(X1) )
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f78]) ).

fof(f78,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( function_inverse(X0) = X1
          <=> ( ! [X2,X3] :
                  ( ( ( apply(X1,X2) = X3
                      & in(X2,relation_rng(X0)) )
                    | apply(X0,X3) != X2
                    | ~ in(X3,relation_dom(X0)) )
                  & sP0(X2,X3,X0,X1) )
              & relation_rng(X0) = relation_dom(X1) ) )
          | ~ function(X1)
          | ~ relation(X1) )
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(definition_folding,[],[f50,f77]) ).

fof(f77,plain,
    ! [X2,X3,X0,X1] :
      ( sP0(X2,X3,X0,X1)
    <=> ( ( apply(X0,X3) = X2
          & in(X3,relation_dom(X0)) )
        | apply(X1,X2) != X3
        | ~ in(X2,relation_rng(X0)) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f50,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( function_inverse(X0) = X1
          <=> ( ! [X2,X3] :
                  ( ( ( apply(X1,X2) = X3
                      & in(X2,relation_rng(X0)) )
                    | apply(X0,X3) != X2
                    | ~ in(X3,relation_dom(X0)) )
                  & ( ( apply(X0,X3) = X2
                      & in(X3,relation_dom(X0)) )
                    | apply(X1,X2) != X3
                    | ~ in(X2,relation_rng(X0)) ) )
              & relation_rng(X0) = relation_dom(X1) ) )
          | ~ function(X1)
          | ~ relation(X1) )
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f49]) ).

fof(f49,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( function_inverse(X0) = X1
          <=> ( ! [X2,X3] :
                  ( ( ( apply(X1,X2) = X3
                      & in(X2,relation_rng(X0)) )
                    | apply(X0,X3) != X2
                    | ~ in(X3,relation_dom(X0)) )
                  & ( ( apply(X0,X3) = X2
                      & in(X3,relation_dom(X0)) )
                    | apply(X1,X2) != X3
                    | ~ in(X2,relation_rng(X0)) ) )
              & relation_rng(X0) = relation_dom(X1) ) )
          | ~ function(X1)
          | ~ relation(X1) )
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f35]) ).

fof(f35,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ( one_to_one(X0)
       => ! [X1] :
            ( ( function(X1)
              & relation(X1) )
           => ( function_inverse(X0) = X1
            <=> ( ! [X2,X3] :
                    ( ( ( apply(X0,X3) = X2
                        & in(X3,relation_dom(X0)) )
                     => ( apply(X1,X2) = X3
                        & in(X2,relation_rng(X0)) ) )
                    & ( ( apply(X1,X2) = X3
                        & in(X2,relation_rng(X0)) )
                     => ( apply(X0,X3) = X2
                        & in(X3,relation_dom(X0)) ) ) )
                & relation_rng(X0) = relation_dom(X1) ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.HQgwq86rBI/Vampire---4.8_20521',t54_funct_1) ).

fof(f246,plain,
    ( in(sK9(function_inverse(sK1)),relation_dom(function_inverse(sK1)))
    | ~ spl14_3 ),
    inference(avatar_component_clause,[],[f244]) ).

fof(f244,plain,
    ( spl14_3
  <=> in(sK9(function_inverse(sK1)),relation_dom(function_inverse(sK1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl14_3])]) ).

fof(f450,plain,
    ( sK10(function_inverse(sK1)) = apply(sK1,apply(function_inverse(sK1),sK9(function_inverse(sK1))))
    | ~ spl14_1
    | ~ spl14_2
    | ~ spl14_4 ),
    inference(forward_demodulation,[],[f449,f272]) ).

fof(f272,plain,
    ( apply(function_inverse(sK1),sK9(function_inverse(sK1))) = apply(function_inverse(sK1),sK10(function_inverse(sK1)))
    | ~ spl14_1
    | ~ spl14_2 ),
    inference(subsumption_resolution,[],[f271,f237]) ).

fof(f271,plain,
    ( apply(function_inverse(sK1),sK9(function_inverse(sK1))) = apply(function_inverse(sK1),sK10(function_inverse(sK1)))
    | ~ relation(function_inverse(sK1))
    | ~ spl14_2 ),
    inference(subsumption_resolution,[],[f270,f241]) ).

fof(f270,plain,
    ( apply(function_inverse(sK1),sK9(function_inverse(sK1))) = apply(function_inverse(sK1),sK10(function_inverse(sK1)))
    | ~ function(function_inverse(sK1))
    | ~ relation(function_inverse(sK1)) ),
    inference(resolution,[],[f146,f112]) ).

fof(f146,plain,
    ! [X0] :
      ( one_to_one(X0)
      | apply(X0,sK9(X0)) = apply(X0,sK10(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f102,plain,
    ! [X0] :
      ( ( ( one_to_one(X0)
          | ( sK9(X0) != sK10(X0)
            & apply(X0,sK9(X0)) = apply(X0,sK10(X0))
            & in(sK10(X0),relation_dom(X0))
            & in(sK9(X0),relation_dom(X0)) ) )
        & ( ! [X3,X4] :
              ( X3 = X4
              | apply(X0,X3) != apply(X0,X4)
              | ~ in(X4,relation_dom(X0))
              | ~ in(X3,relation_dom(X0)) )
          | ~ one_to_one(X0) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f100,f101]) ).

fof(f101,plain,
    ! [X0] :
      ( ? [X1,X2] :
          ( X1 != X2
          & apply(X0,X1) = apply(X0,X2)
          & in(X2,relation_dom(X0))
          & in(X1,relation_dom(X0)) )
     => ( sK9(X0) != sK10(X0)
        & apply(X0,sK9(X0)) = apply(X0,sK10(X0))
        & in(sK10(X0),relation_dom(X0))
        & in(sK9(X0),relation_dom(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f100,plain,
    ! [X0] :
      ( ( ( one_to_one(X0)
          | ? [X1,X2] :
              ( X1 != X2
              & apply(X0,X1) = apply(X0,X2)
              & in(X2,relation_dom(X0))
              & in(X1,relation_dom(X0)) ) )
        & ( ! [X3,X4] :
              ( X3 = X4
              | apply(X0,X3) != apply(X0,X4)
              | ~ in(X4,relation_dom(X0))
              | ~ in(X3,relation_dom(X0)) )
          | ~ one_to_one(X0) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(rectify,[],[f99]) ).

fof(f99,plain,
    ! [X0] :
      ( ( ( one_to_one(X0)
          | ? [X1,X2] :
              ( X1 != X2
              & apply(X0,X1) = apply(X0,X2)
              & in(X2,relation_dom(X0))
              & in(X1,relation_dom(X0)) ) )
        & ( ! [X1,X2] :
              ( X1 = X2
              | apply(X0,X1) != apply(X0,X2)
              | ~ in(X2,relation_dom(X0))
              | ~ in(X1,relation_dom(X0)) )
          | ~ one_to_one(X0) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X0] :
      ( ( one_to_one(X0)
      <=> ! [X1,X2] :
            ( X1 = X2
            | apply(X0,X1) != apply(X0,X2)
            | ~ in(X2,relation_dom(X0))
            | ~ in(X1,relation_dom(X0)) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f55]) ).

fof(f55,plain,
    ! [X0] :
      ( ( one_to_one(X0)
      <=> ! [X1,X2] :
            ( X1 = X2
            | apply(X0,X1) != apply(X0,X2)
            | ~ in(X2,relation_dom(X0))
            | ~ in(X1,relation_dom(X0)) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ( one_to_one(X0)
      <=> ! [X1,X2] :
            ( ( apply(X0,X1) = apply(X0,X2)
              & in(X2,relation_dom(X0))
              & in(X1,relation_dom(X0)) )
           => X1 = X2 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.HQgwq86rBI/Vampire---4.8_20521',d8_funct_1) ).

fof(f449,plain,
    ( sK10(function_inverse(sK1)) = apply(sK1,apply(function_inverse(sK1),sK10(function_inverse(sK1))))
    | ~ spl14_4 ),
    inference(subsumption_resolution,[],[f448,f109]) ).

fof(f448,plain,
    ( sK10(function_inverse(sK1)) = apply(sK1,apply(function_inverse(sK1),sK10(function_inverse(sK1))))
    | ~ relation(sK1)
    | ~ spl14_4 ),
    inference(subsumption_resolution,[],[f447,f110]) ).

fof(f447,plain,
    ( sK10(function_inverse(sK1)) = apply(sK1,apply(function_inverse(sK1),sK10(function_inverse(sK1))))
    | ~ function(sK1)
    | ~ relation(sK1)
    | ~ spl14_4 ),
    inference(subsumption_resolution,[],[f439,f111]) ).

fof(f439,plain,
    ( sK10(function_inverse(sK1)) = apply(sK1,apply(function_inverse(sK1),sK10(function_inverse(sK1))))
    | ~ one_to_one(sK1)
    | ~ function(sK1)
    | ~ relation(sK1)
    | ~ spl14_4 ),
    inference(resolution,[],[f429,f113]) ).

fof(f429,plain,
    ( in(sK10(function_inverse(sK1)),relation_rng(sK1))
    | ~ spl14_4 ),
    inference(backward_demodulation,[],[f263,f425]) ).

fof(f263,plain,
    ( in(sK10(function_inverse(sK1)),relation_dom(function_inverse(sK1)))
    | ~ spl14_4 ),
    inference(avatar_component_clause,[],[f261]) ).

fof(f261,plain,
    ( spl14_4
  <=> in(sK10(function_inverse(sK1)),relation_dom(function_inverse(sK1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl14_4])]) ).

fof(f147,plain,
    ! [X0] :
      ( sK9(X0) != sK10(X0)
      | one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f264,plain,
    ( ~ spl14_2
    | spl14_4
    | ~ spl14_1 ),
    inference(avatar_split_clause,[],[f259,f236,f261,f240]) ).

fof(f259,plain,
    ( in(sK10(function_inverse(sK1)),relation_dom(function_inverse(sK1)))
    | ~ function(function_inverse(sK1))
    | ~ spl14_1 ),
    inference(subsumption_resolution,[],[f253,f237]) ).

fof(f253,plain,
    ( in(sK10(function_inverse(sK1)),relation_dom(function_inverse(sK1)))
    | ~ function(function_inverse(sK1))
    | ~ relation(function_inverse(sK1)) ),
    inference(resolution,[],[f145,f112]) ).

fof(f145,plain,
    ! [X0] :
      ( one_to_one(X0)
      | in(sK10(X0),relation_dom(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f258,plain,
    spl14_2,
    inference(avatar_contradiction_clause,[],[f257]) ).

fof(f257,plain,
    ( $false
    | spl14_2 ),
    inference(subsumption_resolution,[],[f256,f109]) ).

fof(f256,plain,
    ( ~ relation(sK1)
    | spl14_2 ),
    inference(subsumption_resolution,[],[f254,f110]) ).

fof(f254,plain,
    ( ~ function(sK1)
    | ~ relation(sK1)
    | spl14_2 ),
    inference(resolution,[],[f242,f128]) ).

fof(f242,plain,
    ( ~ function(function_inverse(sK1))
    | spl14_2 ),
    inference(avatar_component_clause,[],[f240]) ).

fof(f252,plain,
    spl14_1,
    inference(avatar_contradiction_clause,[],[f251]) ).

fof(f251,plain,
    ( $false
    | spl14_1 ),
    inference(subsumption_resolution,[],[f250,f109]) ).

fof(f250,plain,
    ( ~ relation(sK1)
    | spl14_1 ),
    inference(subsumption_resolution,[],[f248,f110]) ).

fof(f248,plain,
    ( ~ function(sK1)
    | ~ relation(sK1)
    | spl14_1 ),
    inference(resolution,[],[f238,f127]) ).

fof(f238,plain,
    ( ~ relation(function_inverse(sK1))
    | spl14_1 ),
    inference(avatar_component_clause,[],[f236]) ).

fof(f247,plain,
    ( ~ spl14_1
    | ~ spl14_2
    | spl14_3 ),
    inference(avatar_split_clause,[],[f234,f244,f240,f236]) ).

fof(f234,plain,
    ( in(sK9(function_inverse(sK1)),relation_dom(function_inverse(sK1)))
    | ~ function(function_inverse(sK1))
    | ~ relation(function_inverse(sK1)) ),
    inference(resolution,[],[f144,f112]) ).

fof(f144,plain,
    ! [X0] :
      ( one_to_one(X0)
      | in(sK9(X0),relation_dom(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f102]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SEU221+3 : TPTP v8.1.2. Released v3.2.0.
% 0.14/0.15  % 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
% 0.15/0.36  % Computer : n008.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Fri May  3 11:48:27 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36  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.HQgwq86rBI/Vampire---4.8_20521
% 0.57/0.75  % (20866)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.57/0.75  % (20864)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)
% 0.57/0.75  % (20871)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)
% 0.57/0.75  % (20867)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)
% 0.57/0.75  % (20869)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)
% 0.57/0.75  % (20870)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)
% 0.57/0.75  % (20871)Refutation not found, incomplete strategy% (20871)------------------------------
% 0.57/0.75  % (20871)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.75  % (20871)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.75  
% 0.57/0.75  % (20871)Memory used [KB]: 975
% 0.57/0.75  % (20871)Time elapsed: 0.003 s
% 0.57/0.75  % (20871)Instructions burned: 2 (million)
% 0.57/0.75  % (20865)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)
% 0.57/0.75  % (20871)------------------------------
% 0.57/0.75  % (20871)------------------------------
% 0.57/0.75  % (20869)Refutation not found, incomplete strategy% (20869)------------------------------
% 0.57/0.75  % (20869)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.75  % (20869)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.75  
% 0.57/0.75  % (20869)Memory used [KB]: 974
% 0.57/0.75  % (20869)Time elapsed: 0.005 s
% 0.57/0.75  % (20869)Instructions burned: 2 (million)
% 0.57/0.75  % (20869)------------------------------
% 0.57/0.75  % (20869)------------------------------
% 0.57/0.75  % (20864)Refutation not found, incomplete strategy% (20864)------------------------------
% 0.57/0.75  % (20864)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.75  % (20864)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.75  
% 0.57/0.75  % (20864)Memory used [KB]: 1065
% 0.57/0.75  % (20864)Time elapsed: 0.006 s
% 0.57/0.75  % (20864)Instructions burned: 6 (million)
% 0.57/0.75  % (20868)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)
% 0.57/0.75  % (20864)------------------------------
% 0.57/0.75  % (20864)------------------------------
% 0.60/0.75  % (20866)First to succeed.
% 0.60/0.76  % (20868)Refutation not found, incomplete strategy% (20868)------------------------------
% 0.60/0.76  % (20868)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.76  % (20868)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.76  
% 0.60/0.76  % (20868)Memory used [KB]: 1132
% 0.60/0.76  % (20868)Time elapsed: 0.004 s
% 0.60/0.76  % (20868)Instructions burned: 6 (million)
% 0.60/0.76  % (20868)------------------------------
% 0.60/0.76  % (20868)------------------------------
% 0.60/0.76  % (20866)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-20776"
% 0.60/0.76  % (20866)Refutation found. Thanks to Tanya!
% 0.60/0.76  % SZS status Theorem for Vampire---4
% 0.60/0.76  % SZS output start Proof for Vampire---4
% See solution above
% 0.60/0.76  % (20866)------------------------------
% 0.60/0.76  % (20866)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.76  % (20866)Termination reason: Refutation
% 0.60/0.76  
% 0.60/0.76  % (20866)Memory used [KB]: 1212
% 0.60/0.76  % (20866)Time elapsed: 0.011 s
% 0.60/0.76  % (20866)Instructions burned: 25 (million)
% 0.60/0.76  % (20776)Success in time 0.39 s
% 0.60/0.76  % Vampire---4.8 exiting
%------------------------------------------------------------------------------