TSTP Solution File: SEU225+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU225+1 : TPTP v8.2.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n026.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 : Tue May 21 03:55:43 EDT 2024

% Result   : Theorem 47.66s 7.15s
% Output   : Refutation 47.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   65 (   9 unt;   0 def)
%            Number of atoms       :  335 ( 105 equ)
%            Maximal formula atoms :   12 (   5 avg)
%            Number of connectives :  450 ( 180   ~; 188   |;  55   &)
%                                         (  12 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   4 con; 0-2 aty)
%            Number of variables   :  140 ( 127   !;  13   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f52412,plain,
    $false,
    inference(trivial_inequality_removal,[],[f52402]) ).

fof(f52402,plain,
    empty_set != empty_set,
    inference(superposition,[],[f34878,f52400]) ).

fof(f52400,plain,
    empty_set = apply(sK2,sK1),
    inference(resolution,[],[f52399,f109]) ).

fof(f109,plain,
    relation(sK2),
    inference(cnf_transformation,[],[f82]) ).

fof(f82,plain,
    ( apply(relation_dom_restriction(sK2,sK0),sK1) != apply(sK2,sK1)
    & in(sK1,sK0)
    & function(sK2)
    & relation(sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f53,f81]) ).

fof(f81,plain,
    ( ? [X0,X1,X2] :
        ( apply(relation_dom_restriction(X2,X0),X1) != apply(X2,X1)
        & in(X1,X0)
        & function(X2)
        & relation(X2) )
   => ( apply(relation_dom_restriction(sK2,sK0),sK1) != apply(sK2,sK1)
      & in(sK1,sK0)
      & function(sK2)
      & relation(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f53,plain,
    ? [X0,X1,X2] :
      ( apply(relation_dom_restriction(X2,X0),X1) != apply(X2,X1)
      & in(X1,X0)
      & function(X2)
      & relation(X2) ),
    inference(flattening,[],[f52]) ).

fof(f52,plain,
    ? [X0,X1,X2] :
      ( apply(relation_dom_restriction(X2,X0),X1) != apply(X2,X1)
      & in(X1,X0)
      & function(X2)
      & relation(X2) ),
    inference(ennf_transformation,[],[f46]) ).

fof(f46,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ( function(X2)
          & relation(X2) )
       => ( in(X1,X0)
         => apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
    inference(negated_conjecture,[],[f45]) ).

fof(f45,conjecture,
    ! [X0,X1,X2] :
      ( ( function(X2)
        & relation(X2) )
     => ( in(X1,X0)
       => apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_funct_1) ).

fof(f52399,plain,
    ( ~ relation(sK2)
    | empty_set = apply(sK2,sK1) ),
    inference(duplicate_literal_removal,[],[f52397]) ).

fof(f52397,plain,
    ( empty_set = apply(sK2,sK1)
    | ~ relation(sK2)
    | ~ relation(sK2) ),
    inference(resolution,[],[f52347,f140]) ).

fof(f140,plain,
    ! [X0,X1] :
      ( relation(relation_dom_restriction(X0,X1))
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f64]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( relation(relation_dom_restriction(X0,X1))
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X0,X1] :
      ( relation(X0)
     => relation(relation_dom_restriction(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).

fof(f52347,plain,
    ( ~ relation(relation_dom_restriction(sK2,sK0))
    | empty_set = apply(sK2,sK1)
    | ~ relation(sK2) ),
    inference(duplicate_literal_removal,[],[f52346]) ).

fof(f52346,plain,
    ( empty_set = apply(sK2,sK1)
    | ~ relation(relation_dom_restriction(sK2,sK0))
    | ~ relation(sK2)
    | empty_set = apply(sK2,sK1) ),
    inference(forward_demodulation,[],[f52343,f34877]) ).

fof(f34877,plain,
    empty_set = apply(relation_dom_restriction(sK2,sK0),sK1),
    inference(trivial_inequality_removal,[],[f34866]) ).

fof(f34866,plain,
    ( apply(sK2,sK1) != apply(sK2,sK1)
    | empty_set = apply(relation_dom_restriction(sK2,sK0),sK1) ),
    inference(superposition,[],[f112,f34862]) ).

fof(f34862,plain,
    ! [X0,X1] :
      ( apply(sK2,X0) = apply(relation_dom_restriction(sK2,X1),X0)
      | empty_set = apply(relation_dom_restriction(sK2,X1),X0) ),
    inference(resolution,[],[f34861,f109]) ).

fof(f34861,plain,
    ! [X0,X1] :
      ( ~ relation(sK2)
      | apply(sK2,X0) = apply(relation_dom_restriction(sK2,X1),X0)
      | empty_set = apply(relation_dom_restriction(sK2,X1),X0) ),
    inference(duplicate_literal_removal,[],[f34857]) ).

fof(f34857,plain,
    ! [X0,X1] :
      ( apply(sK2,X0) = apply(relation_dom_restriction(sK2,X1),X0)
      | ~ relation(sK2)
      | empty_set = apply(relation_dom_restriction(sK2,X1),X0)
      | ~ relation(sK2) ),
    inference(resolution,[],[f10355,f140]) ).

fof(f10355,plain,
    ! [X0,X1] :
      ( ~ relation(relation_dom_restriction(sK2,X1))
      | apply(sK2,X0) = apply(relation_dom_restriction(sK2,X1),X0)
      | ~ relation(sK2)
      | empty_set = apply(relation_dom_restriction(sK2,X1),X0) ),
    inference(resolution,[],[f2474,f110]) ).

fof(f110,plain,
    function(sK2),
    inference(cnf_transformation,[],[f82]) ).

fof(f2474,plain,
    ! [X2,X0,X1] :
      ( ~ function(X0)
      | ~ relation(X0)
      | apply(X0,X1) = apply(relation_dom_restriction(X0,X2),X1)
      | ~ relation(relation_dom_restriction(X0,X2))
      | empty_set = apply(relation_dom_restriction(X0,X2),X1) ),
    inference(duplicate_literal_removal,[],[f2467]) ).

fof(f2467,plain,
    ! [X2,X0,X1] :
      ( ~ function(X0)
      | ~ relation(X0)
      | apply(X0,X1) = apply(relation_dom_restriction(X0,X2),X1)
      | ~ relation(relation_dom_restriction(X0,X2))
      | empty_set = apply(relation_dom_restriction(X0,X2),X1)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(resolution,[],[f801,f147]) ).

fof(f147,plain,
    ! [X0,X1] :
      ( function(relation_dom_restriction(X0,X1))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( ( function(relation_dom_restriction(X0,X1))
        & relation(relation_dom_restriction(X0,X1)) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f71]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( ( function(relation_dom_restriction(X0,X1))
        & relation(relation_dom_restriction(X0,X1)) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f26,axiom,
    ! [X0,X1] :
      ( ( function(X0)
        & relation(X0) )
     => ( function(relation_dom_restriction(X0,X1))
        & relation(relation_dom_restriction(X0,X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_funct_1) ).

fof(f801,plain,
    ! [X2,X0,X1] :
      ( ~ function(relation_dom_restriction(X0,X2))
      | ~ function(X0)
      | ~ relation(X0)
      | apply(X0,X1) = apply(relation_dom_restriction(X0,X2),X1)
      | ~ relation(relation_dom_restriction(X0,X2))
      | empty_set = apply(relation_dom_restriction(X0,X2),X1) ),
    inference(duplicate_literal_removal,[],[f798]) ).

fof(f798,plain,
    ! [X2,X0,X1] :
      ( apply(X0,X1) = apply(relation_dom_restriction(X0,X2),X1)
      | ~ function(X0)
      | ~ relation(X0)
      | ~ function(relation_dom_restriction(X0,X2))
      | ~ relation(relation_dom_restriction(X0,X2))
      | empty_set = apply(relation_dom_restriction(X0,X2),X1)
      | ~ function(relation_dom_restriction(X0,X2))
      | ~ relation(relation_dom_restriction(X0,X2)) ),
    inference(resolution,[],[f176,f173]) ).

fof(f173,plain,
    ! [X0,X1] :
      ( in(X1,relation_dom(X0))
      | apply(X0,X1) = empty_set
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f130]) ).

fof(f130,plain,
    ! [X2,X0,X1] :
      ( apply(X0,X1) = X2
      | empty_set != X2
      | in(X1,relation_dom(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f83,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( ( ( apply(X0,X1) = X2
                | empty_set != X2 )
              & ( empty_set = X2
                | apply(X0,X1) != X2 ) )
            | in(X1,relation_dom(X0)) )
          & ( ( ( apply(X0,X1) = X2
                | ~ in(ordered_pair(X1,X2),X0) )
              & ( in(ordered_pair(X1,X2),X0)
                | apply(X0,X1) != X2 ) )
            | ~ in(X1,relation_dom(X0)) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f61]) ).

fof(f61,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( ( apply(X0,X1) = X2
            <=> empty_set = X2 )
            | in(X1,relation_dom(X0)) )
          & ( ( apply(X0,X1) = X2
            <=> in(ordered_pair(X1,X2),X0) )
            | ~ in(X1,relation_dom(X0)) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f60]) ).

fof(f60,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( ( apply(X0,X1) = X2
            <=> empty_set = X2 )
            | in(X1,relation_dom(X0)) )
          & ( ( apply(X0,X1) = X2
            <=> in(ordered_pair(X1,X2),X0) )
            | ~ in(X1,relation_dom(X0)) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ! [X1,X2] :
          ( ( ~ in(X1,relation_dom(X0))
           => ( apply(X0,X1) = X2
            <=> empty_set = X2 ) )
          & ( in(X1,relation_dom(X0))
           => ( apply(X0,X1) = X2
            <=> in(ordered_pair(X1,X2),X0) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).

fof(f176,plain,
    ! [X2,X0,X4] :
      ( ~ in(X4,relation_dom(relation_dom_restriction(X2,X0)))
      | apply(X2,X4) = apply(relation_dom_restriction(X2,X0),X4)
      | ~ function(X2)
      | ~ relation(X2)
      | ~ function(relation_dom_restriction(X2,X0))
      | ~ relation(relation_dom_restriction(X2,X0)) ),
    inference(equality_resolution,[],[f149]) ).

fof(f149,plain,
    ! [X2,X0,X1,X4] :
      ( apply(X1,X4) = apply(X2,X4)
      | ~ in(X4,relation_dom(X1))
      | relation_dom_restriction(X2,X0) != X1
      | ~ function(X2)
      | ~ relation(X2)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f90]) ).

fof(f90,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( ( relation_dom_restriction(X2,X0) = X1
              | ( apply(X1,sK4(X1,X2)) != apply(X2,sK4(X1,X2))
                & in(sK4(X1,X2),relation_dom(X1)) )
              | relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
            & ( ( ! [X4] :
                    ( apply(X1,X4) = apply(X2,X4)
                    | ~ in(X4,relation_dom(X1)) )
                & relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
              | relation_dom_restriction(X2,X0) != X1 ) )
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f88,f89]) ).

fof(f89,plain,
    ! [X1,X2] :
      ( ? [X3] :
          ( apply(X1,X3) != apply(X2,X3)
          & in(X3,relation_dom(X1)) )
     => ( apply(X1,sK4(X1,X2)) != apply(X2,sK4(X1,X2))
        & in(sK4(X1,X2),relation_dom(X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f88,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( ( relation_dom_restriction(X2,X0) = X1
              | ? [X3] :
                  ( apply(X1,X3) != apply(X2,X3)
                  & in(X3,relation_dom(X1)) )
              | relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
            & ( ( ! [X4] :
                    ( apply(X1,X4) = apply(X2,X4)
                    | ~ in(X4,relation_dom(X1)) )
                & relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
              | relation_dom_restriction(X2,X0) != X1 ) )
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(rectify,[],[f87]) ).

fof(f87,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( ( relation_dom_restriction(X2,X0) = X1
              | ? [X3] :
                  ( apply(X1,X3) != apply(X2,X3)
                  & in(X3,relation_dom(X1)) )
              | relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
            & ( ( ! [X3] :
                    ( apply(X1,X3) = apply(X2,X3)
                    | ~ in(X3,relation_dom(X1)) )
                & relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
              | relation_dom_restriction(X2,X0) != X1 ) )
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(flattening,[],[f86]) ).

fof(f86,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( ( relation_dom_restriction(X2,X0) = X1
              | ? [X3] :
                  ( apply(X1,X3) != apply(X2,X3)
                  & in(X3,relation_dom(X1)) )
              | relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
            & ( ( ! [X3] :
                    ( apply(X1,X3) = apply(X2,X3)
                    | ~ in(X3,relation_dom(X1)) )
                & relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
              | relation_dom_restriction(X2,X0) != X1 ) )
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(nnf_transformation,[],[f74]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( relation_dom_restriction(X2,X0) = X1
          <=> ( ! [X3] :
                  ( apply(X1,X3) = apply(X2,X3)
                  | ~ in(X3,relation_dom(X1)) )
              & relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(flattening,[],[f73]) ).

fof(f73,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( relation_dom_restriction(X2,X0) = X1
          <=> ( ! [X3] :
                  ( apply(X1,X3) = apply(X2,X3)
                  | ~ in(X3,relation_dom(X1)) )
              & relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(ennf_transformation,[],[f43]) ).

fof(f43,axiom,
    ! [X0,X1] :
      ( ( function(X1)
        & relation(X1) )
     => ! [X2] :
          ( ( function(X2)
            & relation(X2) )
         => ( relation_dom_restriction(X2,X0) = X1
          <=> ( ! [X3] :
                  ( in(X3,relation_dom(X1))
                 => apply(X1,X3) = apply(X2,X3) )
              & relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_funct_1) ).

fof(f112,plain,
    apply(relation_dom_restriction(sK2,sK0),sK1) != apply(sK2,sK1),
    inference(cnf_transformation,[],[f82]) ).

fof(f52343,plain,
    ( ~ relation(relation_dom_restriction(sK2,sK0))
    | ~ relation(sK2)
    | apply(relation_dom_restriction(sK2,sK0),sK1) = apply(sK2,sK1)
    | empty_set = apply(sK2,sK1) ),
    inference(resolution,[],[f39386,f110]) ).

fof(f39386,plain,
    ! [X0] :
      ( ~ function(X0)
      | ~ relation(relation_dom_restriction(X0,sK0))
      | ~ relation(X0)
      | apply(X0,sK1) = apply(relation_dom_restriction(X0,sK0),sK1)
      | empty_set = apply(X0,sK1) ),
    inference(duplicate_literal_removal,[],[f39383]) ).

fof(f39383,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ~ relation(relation_dom_restriction(X0,sK0))
      | ~ function(X0)
      | apply(X0,sK1) = apply(relation_dom_restriction(X0,sK0),sK1)
      | empty_set = apply(X0,sK1)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(resolution,[],[f14508,f147]) ).

fof(f14508,plain,
    ! [X0] :
      ( ~ function(relation_dom_restriction(X0,sK0))
      | ~ relation(X0)
      | ~ relation(relation_dom_restriction(X0,sK0))
      | ~ function(X0)
      | apply(X0,sK1) = apply(relation_dom_restriction(X0,sK0),sK1)
      | empty_set = apply(X0,sK1) ),
    inference(resolution,[],[f2762,f111]) ).

fof(f111,plain,
    in(sK1,sK0),
    inference(cnf_transformation,[],[f82]) ).

fof(f2762,plain,
    ! [X2,X0,X1] :
      ( ~ in(X0,X2)
      | ~ relation(X1)
      | ~ function(relation_dom_restriction(X1,X2))
      | ~ relation(relation_dom_restriction(X1,X2))
      | ~ function(X1)
      | apply(X1,X0) = apply(relation_dom_restriction(X1,X2),X0)
      | empty_set = apply(X1,X0) ),
    inference(duplicate_literal_removal,[],[f2742]) ).

fof(f2742,plain,
    ! [X2,X0,X1] :
      ( ~ in(X0,X2)
      | ~ relation(X1)
      | ~ function(relation_dom_restriction(X1,X2))
      | ~ relation(relation_dom_restriction(X1,X2))
      | ~ function(X1)
      | apply(X1,X0) = apply(relation_dom_restriction(X1,X2),X0)
      | empty_set = apply(X1,X0)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(resolution,[],[f802,f173]) ).

fof(f802,plain,
    ! [X2,X0,X1] :
      ( ~ in(X1,relation_dom(X0))
      | ~ in(X1,X2)
      | ~ relation(X0)
      | ~ function(relation_dom_restriction(X0,X2))
      | ~ relation(relation_dom_restriction(X0,X2))
      | ~ function(X0)
      | apply(X0,X1) = apply(relation_dom_restriction(X0,X2),X1) ),
    inference(duplicate_literal_removal,[],[f797]) ).

fof(f797,plain,
    ! [X2,X0,X1] :
      ( apply(X0,X1) = apply(relation_dom_restriction(X0,X2),X1)
      | ~ function(X0)
      | ~ relation(X0)
      | ~ function(relation_dom_restriction(X0,X2))
      | ~ relation(relation_dom_restriction(X0,X2))
      | ~ in(X1,X2)
      | ~ in(X1,relation_dom(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(resolution,[],[f176,f157]) ).

fof(f157,plain,
    ! [X2,X0,X1] :
      ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
      | ~ in(X1,X0)
      | ~ in(X1,relation_dom(X2))
      | ~ function(X2)
      | ~ relation(X2) ),
    inference(cnf_transformation,[],[f92]) ).

fof(f92,plain,
    ! [X0,X1,X2] :
      ( ( ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
          | ~ in(X1,X0)
          | ~ in(X1,relation_dom(X2)) )
        & ( ( in(X1,X0)
            & in(X1,relation_dom(X2)) )
          | ~ in(X1,relation_dom(relation_dom_restriction(X2,X0))) ) )
      | ~ function(X2)
      | ~ relation(X2) ),
    inference(flattening,[],[f91]) ).

fof(f91,plain,
    ! [X0,X1,X2] :
      ( ( ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
          | ~ in(X1,X0)
          | ~ in(X1,relation_dom(X2)) )
        & ( ( in(X1,X0)
            & in(X1,relation_dom(X2)) )
          | ~ in(X1,relation_dom(relation_dom_restriction(X2,X0))) ) )
      | ~ function(X2)
      | ~ relation(X2) ),
    inference(nnf_transformation,[],[f80]) ).

fof(f80,plain,
    ! [X0,X1,X2] :
      ( ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
      <=> ( in(X1,X0)
          & in(X1,relation_dom(X2)) ) )
      | ~ function(X2)
      | ~ relation(X2) ),
    inference(flattening,[],[f79]) ).

fof(f79,plain,
    ! [X0,X1,X2] :
      ( ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
      <=> ( in(X1,X0)
          & in(X1,relation_dom(X2)) ) )
      | ~ function(X2)
      | ~ relation(X2) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f31,axiom,
    ! [X0,X1,X2] :
      ( ( function(X2)
        & relation(X2) )
     => ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
      <=> ( in(X1,X0)
          & in(X1,relation_dom(X2)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l82_funct_1) ).

fof(f34878,plain,
    empty_set != apply(sK2,sK1),
    inference(backward_demodulation,[],[f112,f34877]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : SEU225+1 : TPTP v8.2.0. Released v3.3.0.
% 0.03/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34  % Computer : n026.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Sun May 19 17:38:53 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  % (9561)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.36  % (9568)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.37  % (9565)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.37  % (9563)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.37  % (9564)WARNING: value z3 for option sas not known
% 0.21/0.37  % (9566)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.21/0.37  TRYING [1]
% 0.21/0.37  % (9564)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.38  TRYING [2]
% 0.21/0.38  TRYING [3]
% 0.21/0.38  % (9562)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.39  % (9567)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.39  TRYING [4]
% 0.21/0.41  TRYING [1]
% 0.21/0.41  TRYING [2]
% 0.21/0.43  TRYING [3]
% 0.21/0.43  TRYING [5]
% 0.21/0.47  TRYING [4]
% 0.21/0.49  TRYING [6]
% 0.21/0.55  TRYING [5]
% 1.66/0.62  TRYING [7]
% 2.84/0.80  TRYING [6]
% 2.84/0.83  TRYING [8]
% 4.17/0.95  TRYING [1]
% 4.17/0.95  TRYING [2]
% 4.17/0.95  TRYING [3]
% 4.28/0.96  TRYING [4]
% 4.28/0.99  TRYING [5]
% 4.68/1.04  TRYING [6]
% 5.09/1.15  TRYING [7]
% 5.72/1.18  TRYING [9]
% 7.31/1.41  TRYING [8]
% 8.39/1.56  TRYING [7]
% 9.98/1.79  TRYING [9]
% 12.10/2.08  TRYING [10]
% 15.23/2.53  TRYING [10]
% 21.57/3.45  TRYING [11]
% 24.69/3.88  TRYING [11]
% 26.69/4.16  TRYING [8]
% 34.85/5.34  TRYING [12]
% 39.07/5.98  TRYING [12]
% 47.52/7.13  % (9567)First to succeed.
% 47.52/7.15  % (9567)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-9561"
% 47.66/7.15  % (9567)Refutation found. Thanks to Tanya!
% 47.66/7.15  % SZS status Theorem for theBenchmark
% 47.66/7.15  % SZS output start Proof for theBenchmark
% See solution above
% 47.66/7.15  % (9567)------------------------------
% 47.66/7.15  % (9567)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 47.66/7.15  % (9567)Termination reason: Refutation
% 47.66/7.15  
% 47.66/7.15  % (9567)Memory used [KB]: 47238
% 47.66/7.15  % (9567)Time elapsed: 6.784 s
% 47.66/7.15  % (9567)Instructions burned: 15927 (million)
% 47.66/7.15  % (9561)Success in time 6.782 s
%------------------------------------------------------------------------------