TSTP Solution File: SET726+4 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET726+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n021.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Aug 31 18:22:00 EDT 2022

% Result   : Theorem 1.52s 0.56s
% Output   : Refutation 1.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   10
% Syntax   : Number of formulae    :  100 (  17 unt;   0 def)
%            Number of atoms       :  443 (  39 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  514 ( 171   ~; 164   |; 133   &)
%                                         (  14 <=>;  32  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   8 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-4 aty)
%            Number of functors    :   12 (  12 usr;   5 con; 0-5 aty)
%            Number of variables   :  353 ( 307   !;  46   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f277,plain,
    $false,
    inference(subsumption_resolution,[],[f276,f98]) ).

fof(f98,plain,
    sK6(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3) != sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),
    inference(resolution,[],[f75,f82]) ).

fof(f82,plain,
    ! [X2,X3,X0,X1] :
      ( equal_maps(X2,X3,X1,X0)
      | sK6(X0,X1,X2,X3) != sK7(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f61,plain,
    ! [X0,X1,X2,X3] :
      ( equal_maps(X2,X3,X1,X0)
      | ( apply(X2,sK8(X0,X1,X2,X3),sK7(X0,X1,X2,X3))
        & sK6(X0,X1,X2,X3) != sK7(X0,X1,X2,X3)
        & apply(X3,sK8(X0,X1,X2,X3),sK6(X0,X1,X2,X3))
        & member(sK7(X0,X1,X2,X3),X0)
        & member(sK6(X0,X1,X2,X3),X0)
        & member(sK8(X0,X1,X2,X3),X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f59,f60]) ).

fof(f60,plain,
    ! [X0,X1,X2,X3] :
      ( ? [X4,X5,X6] :
          ( apply(X2,X6,X5)
          & X4 != X5
          & apply(X3,X6,X4)
          & member(X5,X0)
          & member(X4,X0)
          & member(X6,X1) )
     => ( apply(X2,sK8(X0,X1,X2,X3),sK7(X0,X1,X2,X3))
        & sK6(X0,X1,X2,X3) != sK7(X0,X1,X2,X3)
        & apply(X3,sK8(X0,X1,X2,X3),sK6(X0,X1,X2,X3))
        & member(sK7(X0,X1,X2,X3),X0)
        & member(sK6(X0,X1,X2,X3),X0)
        & member(sK8(X0,X1,X2,X3),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f59,plain,
    ! [X0,X1,X2,X3] :
      ( equal_maps(X2,X3,X1,X0)
      | ? [X4,X5,X6] :
          ( apply(X2,X6,X5)
          & X4 != X5
          & apply(X3,X6,X4)
          & member(X5,X0)
          & member(X4,X0)
          & member(X6,X1) ) ),
    inference(rectify,[],[f48]) ).

fof(f48,plain,
    ! [X0,X1,X3,X2] :
      ( equal_maps(X3,X2,X1,X0)
      | ? [X6,X5,X4] :
          ( apply(X3,X4,X5)
          & X5 != X6
          & apply(X2,X4,X6)
          & member(X5,X0)
          & member(X6,X0)
          & member(X4,X1) ) ),
    inference(flattening,[],[f47]) ).

fof(f47,plain,
    ! [X1,X2,X3,X0] :
      ( equal_maps(X3,X2,X1,X0)
      | ? [X5,X6,X4] :
          ( X5 != X6
          & apply(X3,X4,X5)
          & apply(X2,X4,X6)
          & member(X4,X1)
          & member(X5,X0)
          & member(X6,X0) ) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f38,plain,
    ! [X1,X2,X3,X0] :
      ( ! [X5,X6,X4] :
          ( ( member(X4,X1)
            & member(X5,X0)
            & member(X6,X0) )
         => ( ( apply(X3,X4,X5)
              & apply(X2,X4,X6) )
           => X5 = X6 ) )
     => equal_maps(X3,X2,X1,X0) ),
    inference(unused_predicate_definition_removal,[],[f32]) ).

fof(f32,plain,
    ! [X1,X2,X3,X0] :
      ( equal_maps(X3,X2,X1,X0)
    <=> ! [X5,X6,X4] :
          ( ( member(X4,X1)
            & member(X5,X0)
            & member(X6,X0) )
         => ( ( apply(X3,X4,X5)
              & apply(X2,X4,X6) )
           => X5 = X6 ) ) ),
    inference(rectify,[],[f15]) ).

fof(f15,axiom,
    ! [X1,X0,X9,X5] :
      ( ! [X2,X6,X7] :
          ( ( member(X7,X1)
            & member(X6,X1)
            & member(X2,X0) )
         => ( ( apply(X5,X2,X6)
              & apply(X9,X2,X7) )
           => X6 = X7 ) )
    <=> equal_maps(X5,X9,X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_maps) ).

fof(f75,plain,
    ~ equal_maps(inverse_function(sK2,sK4,sK5),sK3,sK5,sK4),
    inference(cnf_transformation,[],[f58]) ).

fof(f58,plain,
    ( identity(compose_function(sK3,sK2,sK4,sK5,sK4),sK4)
    & identity(compose_function(sK2,sK1,sK5,sK4,sK5),sK5)
    & ~ equal_maps(inverse_function(sK2,sK4,sK5),sK3,sK5,sK4)
    & maps(sK2,sK4,sK5)
    & maps(sK1,sK5,sK4)
    & maps(sK3,sK5,sK4) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5])],[f56,f57]) ).

fof(f57,plain,
    ( ? [X0,X1,X2,X3,X4] :
        ( identity(compose_function(X2,X1,X3,X4,X3),X3)
        & identity(compose_function(X1,X0,X4,X3,X4),X4)
        & ~ equal_maps(inverse_function(X1,X3,X4),X2,X4,X3)
        & maps(X1,X3,X4)
        & maps(X0,X4,X3)
        & maps(X2,X4,X3) )
   => ( identity(compose_function(sK3,sK2,sK4,sK5,sK4),sK4)
      & identity(compose_function(sK2,sK1,sK5,sK4,sK5),sK5)
      & ~ equal_maps(inverse_function(sK2,sK4,sK5),sK3,sK5,sK4)
      & maps(sK2,sK4,sK5)
      & maps(sK1,sK5,sK4)
      & maps(sK3,sK5,sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f56,plain,
    ? [X0,X1,X2,X3,X4] :
      ( identity(compose_function(X2,X1,X3,X4,X3),X3)
      & identity(compose_function(X1,X0,X4,X3,X4),X4)
      & ~ equal_maps(inverse_function(X1,X3,X4),X2,X4,X3)
      & maps(X1,X3,X4)
      & maps(X0,X4,X3)
      & maps(X2,X4,X3) ),
    inference(rectify,[],[f46]) ).

fof(f46,plain,
    ? [X2,X1,X3,X4,X0] :
      ( identity(compose_function(X3,X1,X4,X0,X4),X4)
      & identity(compose_function(X1,X2,X0,X4,X0),X0)
      & ~ equal_maps(inverse_function(X1,X4,X0),X3,X0,X4)
      & maps(X1,X4,X0)
      & maps(X2,X0,X4)
      & maps(X3,X0,X4) ),
    inference(flattening,[],[f45]) ).

fof(f45,plain,
    ? [X1,X0,X2,X3,X4] :
      ( ~ equal_maps(inverse_function(X1,X4,X0),X3,X0,X4)
      & maps(X3,X0,X4)
      & maps(X1,X4,X0)
      & identity(compose_function(X3,X1,X4,X0,X4),X4)
      & identity(compose_function(X1,X2,X0,X4,X0),X0)
      & maps(X2,X0,X4) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f31,plain,
    ~ ! [X1,X0,X2,X3,X4] :
        ( ( maps(X3,X0,X4)
          & maps(X1,X4,X0)
          & identity(compose_function(X3,X1,X4,X0,X4),X4)
          & identity(compose_function(X1,X2,X0,X4,X0),X0)
          & maps(X2,X0,X4) )
       => equal_maps(inverse_function(X1,X4,X0),X3,X0,X4) ),
    inference(rectify,[],[f30]) ).

fof(f30,negated_conjecture,
    ~ ! [X1,X5,X8,X9,X0] :
        ( ( maps(X5,X0,X1)
          & maps(X9,X1,X0)
          & maps(X8,X1,X0)
          & identity(compose_function(X9,X5,X0,X1,X0),X0)
          & identity(compose_function(X5,X8,X1,X0,X1),X1) )
       => equal_maps(inverse_function(X5,X0,X1),X9,X1,X0) ),
    inference(negated_conjecture,[],[f29]) ).

fof(f29,conjecture,
    ! [X1,X5,X8,X9,X0] :
      ( ( maps(X5,X0,X1)
        & maps(X9,X1,X0)
        & maps(X8,X1,X0)
        & identity(compose_function(X9,X5,X0,X1,X0),X0)
        & identity(compose_function(X5,X8,X1,X0,X1),X1) )
     => equal_maps(inverse_function(X5,X0,X1),X9,X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII17) ).

fof(f276,plain,
    sK6(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3) = sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),
    inference(forward_demodulation,[],[f275,f151]) ).

fof(f151,plain,
    sK0(sK4,sK3,sK8(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3)) = sK6(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),
    inference(subsumption_resolution,[],[f150,f101]) ).

fof(f101,plain,
    member(sK6(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK4),
    inference(resolution,[],[f75,f79]) ).

fof(f79,plain,
    ! [X2,X3,X0,X1] :
      ( equal_maps(X2,X3,X1,X0)
      | member(sK6(X0,X1,X2,X3),X0) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f150,plain,
    ( sK0(sK4,sK3,sK8(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3)) = sK6(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3)
    | ~ member(sK6(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK4) ),
    inference(subsumption_resolution,[],[f146,f102]) ).

fof(f102,plain,
    member(sK8(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK5),
    inference(resolution,[],[f75,f78]) ).

fof(f78,plain,
    ! [X2,X3,X0,X1] :
      ( equal_maps(X2,X3,X1,X0)
      | member(sK8(X0,X1,X2,X3),X1) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f146,plain,
    ( ~ member(sK8(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK5)
    | ~ member(sK6(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK4)
    | sK0(sK4,sK3,sK8(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3)) = sK6(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3) ),
    inference(resolution,[],[f121,f99]) ).

fof(f99,plain,
    apply(sK3,sK8(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK6(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3)),
    inference(resolution,[],[f75,f81]) ).

fof(f81,plain,
    ! [X2,X3,X0,X1] :
      ( equal_maps(X2,X3,X1,X0)
      | apply(X3,sK8(X0,X1,X2,X3),sK6(X0,X1,X2,X3)) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f121,plain,
    ! [X0,X1] :
      ( ~ apply(sK3,X0,X1)
      | ~ member(X0,sK5)
      | sK0(sK4,sK3,X0) = X1
      | ~ member(X1,sK4) ),
    inference(subsumption_resolution,[],[f120,f91]) ).

fof(f91,plain,
    ! [X4] :
      ( member(sK0(sK4,sK3,X4),sK4)
      | ~ member(X4,sK5) ),
    inference(resolution,[],[f72,f68]) ).

fof(f68,plain,
    ! [X2,X3,X0,X1] :
      ( ~ maps(X1,X2,X0)
      | ~ member(X3,X2)
      | member(sK0(X0,X1,X3),X0) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f53,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ~ member(X3,X2)
            | ( apply(X1,X3,sK0(X0,X1,X3))
              & member(sK0(X0,X1,X3),X0) ) )
        & ! [X5,X6,X7] :
            ( X5 = X7
            | ~ member(X7,X0)
            | ~ apply(X1,X6,X5)
            | ~ member(X5,X0)
            | ~ apply(X1,X6,X7)
            | ~ member(X6,X2) ) )
      | ~ maps(X1,X2,X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f51,f52]) ).

fof(f52,plain,
    ! [X0,X1,X3] :
      ( ? [X4] :
          ( apply(X1,X3,X4)
          & member(X4,X0) )
     => ( apply(X1,X3,sK0(X0,X1,X3))
        & member(sK0(X0,X1,X3),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f51,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ~ member(X3,X2)
            | ? [X4] :
                ( apply(X1,X3,X4)
                & member(X4,X0) ) )
        & ! [X5,X6,X7] :
            ( X5 = X7
            | ~ member(X7,X0)
            | ~ apply(X1,X6,X5)
            | ~ member(X5,X0)
            | ~ apply(X1,X6,X7)
            | ~ member(X6,X2) ) )
      | ~ maps(X1,X2,X0) ),
    inference(rectify,[],[f44]) ).

fof(f44,plain,
    ! [X0,X2,X1] :
      ( ( ! [X6] :
            ( ~ member(X6,X1)
            | ? [X7] :
                ( apply(X2,X6,X7)
                & member(X7,X0) ) )
        & ! [X5,X4,X3] :
            ( X3 = X5
            | ~ member(X3,X0)
            | ~ apply(X2,X4,X5)
            | ~ member(X5,X0)
            | ~ apply(X2,X4,X3)
            | ~ member(X4,X1) ) )
      | ~ maps(X2,X1,X0) ),
    inference(flattening,[],[f43]) ).

fof(f43,plain,
    ! [X2,X1,X0] :
      ( ( ! [X3,X5,X4] :
            ( X3 = X5
            | ~ apply(X2,X4,X5)
            | ~ apply(X2,X4,X3)
            | ~ member(X4,X1)
            | ~ member(X5,X0)
            | ~ member(X3,X0) )
        & ! [X6] :
            ( ~ member(X6,X1)
            | ? [X7] :
                ( apply(X2,X6,X7)
                & member(X7,X0) ) ) )
      | ~ maps(X2,X1,X0) ),
    inference(ennf_transformation,[],[f39]) ).

fof(f39,plain,
    ! [X2,X1,X0] :
      ( maps(X2,X1,X0)
     => ( ! [X3,X5,X4] :
            ( ( member(X4,X1)
              & member(X5,X0)
              & member(X3,X0) )
           => ( ( apply(X2,X4,X5)
                & apply(X2,X4,X3) )
             => X3 = X5 ) )
        & ! [X6] :
            ( member(X6,X1)
           => ? [X7] :
                ( apply(X2,X6,X7)
                & member(X7,X0) ) ) ) ),
    inference(unused_predicate_definition_removal,[],[f34]) ).

fof(f34,plain,
    ! [X2,X1,X0] :
      ( ( ! [X3,X5,X4] :
            ( ( member(X4,X1)
              & member(X5,X0)
              & member(X3,X0) )
           => ( ( apply(X2,X4,X5)
                & apply(X2,X4,X3) )
             => X3 = X5 ) )
        & ! [X6] :
            ( member(X6,X1)
           => ? [X7] :
                ( apply(X2,X6,X7)
                & member(X7,X0) ) ) )
    <=> maps(X2,X1,X0) ),
    inference(rectify,[],[f12]) ).

fof(f12,axiom,
    ! [X1,X0,X5] :
      ( ( ! [X7,X2,X6] :
            ( ( member(X7,X1)
              & member(X6,X1)
              & member(X2,X0) )
           => ( ( apply(X5,X2,X6)
                & apply(X5,X2,X7) )
             => X6 = X7 ) )
        & ! [X2] :
            ( member(X2,X0)
           => ? [X4] :
                ( member(X4,X1)
                & apply(X5,X2,X4) ) ) )
    <=> maps(X5,X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps) ).

fof(f72,plain,
    maps(sK3,sK5,sK4),
    inference(cnf_transformation,[],[f58]) ).

fof(f120,plain,
    ! [X0,X1] :
      ( ~ apply(sK3,X0,X1)
      | ~ member(X1,sK4)
      | ~ member(sK0(sK4,sK3,X0),sK4)
      | sK0(sK4,sK3,X0) = X1
      | ~ member(X0,sK5) ),
    inference(duplicate_literal_removal,[],[f118]) ).

fof(f118,plain,
    ! [X0,X1] :
      ( ~ member(X1,sK4)
      | ~ member(X0,sK5)
      | ~ member(sK0(sK4,sK3,X0),sK4)
      | ~ member(X0,sK5)
      | sK0(sK4,sK3,X0) = X1
      | ~ apply(sK3,X0,X1) ),
    inference(resolution,[],[f89,f90]) ).

fof(f90,plain,
    ! [X3] :
      ( apply(sK3,X3,sK0(sK4,sK3,X3))
      | ~ member(X3,sK5) ),
    inference(resolution,[],[f72,f69]) ).

fof(f69,plain,
    ! [X2,X3,X0,X1] :
      ( ~ maps(X1,X2,X0)
      | ~ member(X3,X2)
      | apply(X1,X3,sK0(X0,X1,X3)) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f89,plain,
    ! [X2,X0,X1] :
      ( ~ apply(sK3,X2,X1)
      | ~ apply(sK3,X2,X0)
      | ~ member(X0,sK4)
      | X0 = X1
      | ~ member(X2,sK5)
      | ~ member(X1,sK4) ),
    inference(resolution,[],[f72,f67]) ).

fof(f67,plain,
    ! [X2,X0,X1,X6,X7,X5] :
      ( ~ maps(X1,X2,X0)
      | X5 = X7
      | ~ member(X6,X2)
      | ~ member(X5,X0)
      | ~ apply(X1,X6,X5)
      | ~ member(X7,X0)
      | ~ apply(X1,X6,X7) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f275,plain,
    sK0(sK4,sK3,sK8(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3)) = sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),
    inference(forward_demodulation,[],[f156,f213]) ).

fof(f213,plain,
    sK9(sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK5,sK2,sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK3) = sK8(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),
    inference(subsumption_resolution,[],[f212,f100]) ).

fof(f100,plain,
    member(sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK4),
    inference(resolution,[],[f75,f80]) ).

fof(f80,plain,
    ! [X2,X3,X0,X1] :
      ( equal_maps(X2,X3,X1,X0)
      | member(sK7(X0,X1,X2,X3),X0) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f212,plain,
    ( ~ member(sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK4)
    | sK9(sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK5,sK2,sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK3) = sK8(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3) ),
    inference(subsumption_resolution,[],[f207,f102]) ).

fof(f207,plain,
    ( sK9(sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK5,sK2,sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK3) = sK8(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3)
    | ~ member(sK8(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK5)
    | ~ member(sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK4) ),
    inference(resolution,[],[f144,f138]) ).

fof(f138,plain,
    apply(sK2,sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK8(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3)),
    inference(subsumption_resolution,[],[f137,f102]) ).

fof(f137,plain,
    ( ~ member(sK8(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK5)
    | apply(sK2,sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK8(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3)) ),
    inference(subsumption_resolution,[],[f136,f100]) ).

fof(f136,plain,
    ( ~ member(sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK4)
    | ~ member(sK8(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK5)
    | apply(sK2,sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK8(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3)) ),
    inference(resolution,[],[f103,f70]) ).

fof(f70,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ apply(inverse_function(X3,X0,X2),X1,X4)
      | ~ member(X4,X0)
      | apply(X3,X4,X1)
      | ~ member(X1,X2) ),
    inference(cnf_transformation,[],[f55]) ).

fof(f55,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ member(X1,X2)
      | ~ member(X4,X0)
      | ( ( apply(inverse_function(X3,X0,X2),X1,X4)
          | ~ apply(X3,X4,X1) )
        & ( apply(X3,X4,X1)
          | ~ apply(inverse_function(X3,X0,X2),X1,X4) ) ) ),
    inference(rectify,[],[f54]) ).

fof(f54,plain,
    ! [X0,X2,X4,X3,X1] :
      ( ~ member(X2,X4)
      | ~ member(X1,X0)
      | ( ( apply(inverse_function(X3,X0,X4),X2,X1)
          | ~ apply(X3,X1,X2) )
        & ( apply(X3,X1,X2)
          | ~ apply(inverse_function(X3,X0,X4),X2,X1) ) ) ),
    inference(nnf_transformation,[],[f42]) ).

fof(f42,plain,
    ! [X0,X2,X4,X3,X1] :
      ( ~ member(X2,X4)
      | ~ member(X1,X0)
      | ( apply(inverse_function(X3,X0,X4),X2,X1)
      <=> apply(X3,X1,X2) ) ),
    inference(flattening,[],[f41]) ).

fof(f41,plain,
    ! [X4,X2,X3,X1,X0] :
      ( ( apply(inverse_function(X3,X0,X4),X2,X1)
      <=> apply(X3,X1,X2) )
      | ~ member(X2,X4)
      | ~ member(X1,X0) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X4,X2,X3,X1,X0] :
      ( ( member(X2,X4)
        & member(X1,X0) )
     => ( apply(inverse_function(X3,X0,X4),X2,X1)
      <=> apply(X3,X1,X2) ) ),
    inference(rectify,[],[f21]) ).

fof(f21,axiom,
    ! [X0,X2,X4,X5,X1] :
      ( ( member(X4,X1)
        & member(X2,X0) )
     => ( apply(X5,X2,X4)
      <=> apply(inverse_function(X5,X0,X1),X4,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_function) ).

fof(f103,plain,
    apply(inverse_function(sK2,sK4,sK5),sK8(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3)),
    inference(resolution,[],[f75,f83]) ).

fof(f83,plain,
    ! [X2,X3,X0,X1] :
      ( equal_maps(X2,X3,X1,X0)
      | apply(X2,sK8(X0,X1,X2,X3),sK7(X0,X1,X2,X3)) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f144,plain,
    ! [X0,X1] :
      ( ~ apply(sK2,X0,X1)
      | ~ member(X0,sK4)
      | ~ member(X1,sK5)
      | sK9(X0,sK5,sK2,X0,sK3) = X1 ),
    inference(subsumption_resolution,[],[f143,f117]) ).

fof(f117,plain,
    ! [X1] :
      ( member(sK9(X1,sK5,sK2,X1,sK3),sK5)
      | ~ member(X1,sK4) ),
    inference(duplicate_literal_removal,[],[f113]) ).

fof(f113,plain,
    ! [X1] :
      ( ~ member(X1,sK4)
      | member(sK9(X1,sK5,sK2,X1,sK3),sK5)
      | ~ member(X1,sK4)
      | ~ member(X1,sK4) ),
    inference(resolution,[],[f105,f87]) ).

fof(f87,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ apply(compose_function(X6,X2,X4,X1,X5),X3,X0)
      | member(sK9(X0,X1,X2,X3,X6),X1)
      | ~ member(X3,X4)
      | ~ member(X0,X5) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f65,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ~ member(X3,X4)
      | ( ( ( member(sK9(X0,X1,X2,X3,X6),X1)
            & apply(X6,sK9(X0,X1,X2,X3,X6),X0)
            & apply(X2,X3,sK9(X0,X1,X2,X3,X6)) )
          | ~ apply(compose_function(X6,X2,X4,X1,X5),X3,X0) )
        & ( apply(compose_function(X6,X2,X4,X1,X5),X3,X0)
          | ! [X8] :
              ( ~ member(X8,X1)
              | ~ apply(X6,X8,X0)
              | ~ apply(X2,X3,X8) ) ) )
      | ~ member(X0,X5) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f63,f64]) ).

fof(f64,plain,
    ! [X0,X1,X2,X3,X6] :
      ( ? [X7] :
          ( member(X7,X1)
          & apply(X6,X7,X0)
          & apply(X2,X3,X7) )
     => ( member(sK9(X0,X1,X2,X3,X6),X1)
        & apply(X6,sK9(X0,X1,X2,X3,X6),X0)
        & apply(X2,X3,sK9(X0,X1,X2,X3,X6)) ) ),
    introduced(choice_axiom,[]) ).

fof(f63,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ~ member(X3,X4)
      | ( ( ? [X7] :
              ( member(X7,X1)
              & apply(X6,X7,X0)
              & apply(X2,X3,X7) )
          | ~ apply(compose_function(X6,X2,X4,X1,X5),X3,X0) )
        & ( apply(compose_function(X6,X2,X4,X1,X5),X3,X0)
          | ! [X8] :
              ( ~ member(X8,X1)
              | ~ apply(X6,X8,X0)
              | ~ apply(X2,X3,X8) ) ) )
      | ~ member(X0,X5) ),
    inference(rectify,[],[f62]) ).

fof(f62,plain,
    ! [X2,X6,X1,X5,X4,X0,X3] :
      ( ~ member(X5,X4)
      | ( ( ? [X7] :
              ( member(X7,X6)
              & apply(X3,X7,X2)
              & apply(X1,X5,X7) )
          | ~ apply(compose_function(X3,X1,X4,X6,X0),X5,X2) )
        & ( apply(compose_function(X3,X1,X4,X6,X0),X5,X2)
          | ! [X7] :
              ( ~ member(X7,X6)
              | ~ apply(X3,X7,X2)
              | ~ apply(X1,X5,X7) ) ) )
      | ~ member(X2,X0) ),
    inference(nnf_transformation,[],[f50]) ).

fof(f50,plain,
    ! [X2,X6,X1,X5,X4,X0,X3] :
      ( ~ member(X5,X4)
      | ( ? [X7] :
            ( member(X7,X6)
            & apply(X3,X7,X2)
            & apply(X1,X5,X7) )
      <=> apply(compose_function(X3,X1,X4,X6,X0),X5,X2) )
      | ~ member(X2,X0) ),
    inference(flattening,[],[f49]) ).

fof(f49,plain,
    ! [X3,X4,X5,X2,X1,X6,X0] :
      ( ( ? [X7] :
            ( member(X7,X6)
            & apply(X3,X7,X2)
            & apply(X1,X5,X7) )
      <=> apply(compose_function(X3,X1,X4,X6,X0),X5,X2) )
      | ~ member(X2,X0)
      | ~ member(X5,X4) ),
    inference(ennf_transformation,[],[f36]) ).

fof(f36,plain,
    ! [X3,X4,X5,X2,X1,X6,X0] :
      ( ( member(X2,X0)
        & member(X5,X4) )
     => ( ? [X7] :
            ( member(X7,X6)
            & apply(X3,X7,X2)
            & apply(X1,X5,X7) )
      <=> apply(compose_function(X3,X1,X4,X6,X0),X5,X2) ) ),
    inference(rectify,[],[f14]) ).

fof(f14,axiom,
    ! [X10,X5,X11,X9,X0,X2,X1] :
      ( ( member(X11,X10)
        & member(X2,X0) )
     => ( apply(compose_function(X9,X5,X0,X1,X10),X2,X11)
      <=> ? [X4] :
            ( member(X4,X1)
            & apply(X9,X4,X11)
            & apply(X5,X2,X4) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_function) ).

fof(f105,plain,
    ! [X0] :
      ( apply(compose_function(sK3,sK2,sK4,sK5,sK4),X0,X0)
      | ~ member(X0,sK4) ),
    inference(resolution,[],[f77,f88]) ).

fof(f88,plain,
    ! [X2,X0,X1] :
      ( ~ identity(X0,X1)
      | apply(X0,X2,X2)
      | ~ member(X2,X1) ),
    inference(cnf_transformation,[],[f66]) ).

fof(f66,plain,
    ! [X0,X1] :
      ( ~ identity(X0,X1)
      | ! [X2] :
          ( apply(X0,X2,X2)
          | ~ member(X2,X1) ) ),
    inference(rectify,[],[f40]) ).

fof(f40,plain,
    ! [X1,X0] :
      ( ~ identity(X1,X0)
      | ! [X2] :
          ( apply(X1,X2,X2)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X1,X0] :
      ( identity(X1,X0)
     => ! [X2] :
          ( member(X2,X0)
         => apply(X1,X2,X2) ) ),
    inference(unused_predicate_definition_removal,[],[f35]) ).

fof(f35,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( member(X2,X0)
         => apply(X1,X2,X2) )
    <=> identity(X1,X0) ),
    inference(rectify,[],[f16]) ).

fof(f16,axiom,
    ! [X0,X5] :
      ( identity(X5,X0)
    <=> ! [X2] :
          ( member(X2,X0)
         => apply(X5,X2,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).

fof(f77,plain,
    identity(compose_function(sK3,sK2,sK4,sK5,sK4),sK4),
    inference(cnf_transformation,[],[f58]) ).

fof(f143,plain,
    ! [X0,X1] :
      ( sK9(X0,sK5,sK2,X0,sK3) = X1
      | ~ member(X0,sK4)
      | ~ apply(sK2,X0,X1)
      | ~ member(sK9(X0,sK5,sK2,X0,sK3),sK5)
      | ~ member(X1,sK5) ),
    inference(duplicate_literal_removal,[],[f142]) ).

fof(f142,plain,
    ! [X0,X1] :
      ( ~ member(sK9(X0,sK5,sK2,X0,sK3),sK5)
      | ~ member(X1,sK5)
      | ~ member(X0,sK4)
      | sK9(X0,sK5,sK2,X0,sK3) = X1
      | ~ apply(sK2,X0,X1)
      | ~ member(X0,sK4) ),
    inference(resolution,[],[f116,f95]) ).

fof(f95,plain,
    ! [X2,X0,X1] :
      ( ~ apply(sK2,X2,X0)
      | ~ apply(sK2,X2,X1)
      | ~ member(X2,sK4)
      | X0 = X1
      | ~ member(X1,sK5)
      | ~ member(X0,sK5) ),
    inference(resolution,[],[f74,f67]) ).

fof(f74,plain,
    maps(sK2,sK4,sK5),
    inference(cnf_transformation,[],[f58]) ).

fof(f116,plain,
    ! [X2] :
      ( apply(sK2,X2,sK9(X2,sK5,sK2,X2,sK3))
      | ~ member(X2,sK4) ),
    inference(duplicate_literal_removal,[],[f114]) ).

fof(f114,plain,
    ! [X2] :
      ( ~ member(X2,sK4)
      | ~ member(X2,sK4)
      | apply(sK2,X2,sK9(X2,sK5,sK2,X2,sK3))
      | ~ member(X2,sK4) ),
    inference(resolution,[],[f105,f85]) ).

fof(f85,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ apply(compose_function(X6,X2,X4,X1,X5),X3,X0)
      | apply(X2,X3,sK9(X0,X1,X2,X3,X6))
      | ~ member(X0,X5)
      | ~ member(X3,X4) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f156,plain,
    sK0(sK4,sK3,sK9(sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK5,sK2,sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK3)) = sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),
    inference(resolution,[],[f152,f100]) ).

fof(f152,plain,
    ! [X1] :
      ( ~ member(X1,sK4)
      | sK0(sK4,sK3,sK9(X1,sK5,sK2,X1,sK3)) = X1 ),
    inference(subsumption_resolution,[],[f149,f117]) ).

fof(f149,plain,
    ! [X1] :
      ( ~ member(sK9(X1,sK5,sK2,X1,sK3),sK5)
      | sK0(sK4,sK3,sK9(X1,sK5,sK2,X1,sK3)) = X1
      | ~ member(X1,sK4) ),
    inference(duplicate_literal_removal,[],[f147]) ).

fof(f147,plain,
    ! [X1] :
      ( ~ member(X1,sK4)
      | ~ member(sK9(X1,sK5,sK2,X1,sK3),sK5)
      | sK0(sK4,sK3,sK9(X1,sK5,sK2,X1,sK3)) = X1
      | ~ member(X1,sK4) ),
    inference(resolution,[],[f121,f115]) ).

fof(f115,plain,
    ! [X0] :
      ( apply(sK3,sK9(X0,sK5,sK2,X0,sK3),X0)
      | ~ member(X0,sK4) ),
    inference(duplicate_literal_removal,[],[f112]) ).

fof(f112,plain,
    ! [X0] :
      ( ~ member(X0,sK4)
      | ~ member(X0,sK4)
      | ~ member(X0,sK4)
      | apply(sK3,sK9(X0,sK5,sK2,X0,sK3),X0) ),
    inference(resolution,[],[f105,f86]) ).

fof(f86,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ apply(compose_function(X6,X2,X4,X1,X5),X3,X0)
      | ~ member(X0,X5)
      | ~ member(X3,X4)
      | apply(X6,sK9(X0,X1,X2,X3,X6),X0) ),
    inference(cnf_transformation,[],[f65]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem    : SET726+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.06/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.33  % Computer : n021.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Tue Aug 30 14:12:11 EDT 2022
% 0.13/0.33  % CPUTime    : 
% 0.19/0.48  % (14931)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.49  % (14939)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.50  % (14939)Instruction limit reached!
% 0.19/0.50  % (14939)------------------------------
% 0.19/0.50  % (14939)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50  % (14939)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50  % (14939)Termination reason: Unknown
% 0.19/0.50  % (14939)Termination phase: Property scanning
% 0.19/0.50  
% 0.19/0.50  % (14939)Memory used [KB]: 1535
% 0.19/0.50  % (14939)Time elapsed: 0.004 s
% 0.19/0.50  % (14939)Instructions burned: 3 (million)
% 0.19/0.50  % (14939)------------------------------
% 0.19/0.50  % (14939)------------------------------
% 0.19/0.51  % (14930)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.19/0.52  % (14931)Instruction limit reached!
% 0.19/0.52  % (14931)------------------------------
% 0.19/0.52  % (14931)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (14931)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (14931)Termination reason: Unknown
% 0.19/0.52  % (14931)Termination phase: Saturation
% 0.19/0.52  
% 0.19/0.52  % (14931)Memory used [KB]: 6524
% 0.19/0.52  % (14931)Time elapsed: 0.112 s
% 0.19/0.52  % (14931)Instructions burned: 39 (million)
% 0.19/0.52  % (14931)------------------------------
% 0.19/0.52  % (14931)------------------------------
% 0.19/0.53  % (14947)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.19/0.53  % (14940)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.53  % (14930)First to succeed.
% 0.19/0.54  % (14954)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 0.19/0.54  % (14932)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.54  % (14946)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.55  % (14948)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.19/0.55  % (14938)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.55  % (14940)Instruction limit reached!
% 0.19/0.55  % (14940)------------------------------
% 0.19/0.55  % (14940)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.55  % (14940)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.55  % (14940)Termination reason: Unknown
% 0.19/0.55  % (14940)Termination phase: Saturation
% 0.19/0.55  
% 0.19/0.55  % (14940)Memory used [KB]: 6140
% 0.19/0.55  % (14940)Time elapsed: 0.101 s
% 0.19/0.55  % (14940)Instructions burned: 7 (million)
% 0.19/0.55  % (14940)------------------------------
% 0.19/0.55  % (14940)------------------------------
% 1.52/0.56  % (14930)Refutation found. Thanks to Tanya!
% 1.52/0.56  % SZS status Theorem for theBenchmark
% 1.52/0.56  % SZS output start Proof for theBenchmark
% See solution above
% 1.52/0.56  % (14930)------------------------------
% 1.52/0.56  % (14930)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.52/0.56  % (14930)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.52/0.56  % (14930)Termination reason: Refutation
% 1.52/0.56  
% 1.52/0.56  % (14930)Memory used [KB]: 1663
% 1.52/0.56  % (14930)Time elapsed: 0.138 s
% 1.52/0.56  % (14930)Instructions burned: 13 (million)
% 1.52/0.56  % (14930)------------------------------
% 1.52/0.56  % (14930)------------------------------
% 1.52/0.56  % (14923)Success in time 0.215 s
%------------------------------------------------------------------------------