TSTP Solution File: SEU039+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SEU039+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n020.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 : Thu Aug 31 17:03:29 EDT 2023

% Result   : Theorem 3.69s 1.09s
% Output   : CNFRefutation 3.69s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   78 (  15 unt;   0 def)
%            Number of atoms       :  404 (  95 equ)
%            Maximal formula atoms :   16 (   5 avg)
%            Number of connectives :  532 ( 206   ~; 197   |; 100   &)
%                                         (  11 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   3 con; 0-3 aty)
%            Number of variables   :  190 (   2 sgn; 138   !;  31   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f6,axiom,
    ! [X0,X1,X2] :
      ( set_intersection2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            & in(X3,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).

fof(f7,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ! [X1] :
          ( relation_rng(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] :
                  ( apply(X0,X3) = X2
                  & in(X3,relation_dom(X0)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).

fof(f8,axiom,
    ! [X0,X1] :
      ( relation(X0)
     => relation(relation_dom_restriction(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).

fof(f15,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(f39,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(f41,axiom,
    ! [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(f42,conjecture,
    ! [X0,X1,X2] :
      ( ( function(X2)
        & relation(X2) )
     => ( ( in(X1,X0)
          & in(X1,relation_dom(X2)) )
       => in(apply(X2,X1),relation_rng(relation_dom_restriction(X2,X0))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_funct_1) ).

fof(f43,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ( function(X2)
          & relation(X2) )
       => ( ( in(X1,X0)
            & in(X1,relation_dom(X2)) )
         => in(apply(X2,X1),relation_rng(relation_dom_restriction(X2,X0))) ) ),
    inference(negated_conjecture,[],[f42]) ).

fof(f56,plain,
    ! [X0] :
      ( ! [X1] :
          ( relation_rng(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] :
                  ( apply(X0,X3) = X2
                  & in(X3,relation_dom(X0)) ) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f57,plain,
    ! [X0] :
      ( ! [X1] :
          ( relation_rng(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] :
                  ( apply(X0,X3) = X2
                  & in(X3,relation_dom(X0)) ) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f56]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( relation(relation_dom_restriction(X0,X1))
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( ( function(relation_dom_restriction(X0,X1))
        & relation(relation_dom_restriction(X0,X1)) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( ( function(relation_dom_restriction(X0,X1))
        & relation(relation_dom_restriction(X0,X1)) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f63]) ).

fof(f79,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,[],[f39]) ).

fof(f80,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,[],[f79]) ).

fof(f82,plain,
    ! [X0,X1,X2] :
      ( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
      | ~ in(X1,X0)
      | ~ function(X2)
      | ~ relation(X2) ),
    inference(ennf_transformation,[],[f41]) ).

fof(f83,plain,
    ! [X0,X1,X2] :
      ( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
      | ~ in(X1,X0)
      | ~ function(X2)
      | ~ relation(X2) ),
    inference(flattening,[],[f82]) ).

fof(f84,plain,
    ? [X0,X1,X2] :
      ( ~ in(apply(X2,X1),relation_rng(relation_dom_restriction(X2,X0)))
      & in(X1,X0)
      & in(X1,relation_dom(X2))
      & function(X2)
      & relation(X2) ),
    inference(ennf_transformation,[],[f43]) ).

fof(f85,plain,
    ? [X0,X1,X2] :
      ( ~ in(apply(X2,X1),relation_rng(relation_dom_restriction(X2,X0)))
      & in(X1,X0)
      & in(X1,relation_dom(X2))
      & function(X2)
      & relation(X2) ),
    inference(flattening,[],[f84]) ).

fof(f88,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) = X2
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ~ in(X3,X1)
              | ~ in(X3,X0) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | ~ in(X3,X2) ) )
        | set_intersection2(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f6]) ).

fof(f89,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) = X2
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ~ in(X3,X1)
              | ~ in(X3,X0) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | ~ in(X3,X2) ) )
        | set_intersection2(X0,X1) != X2 ) ),
    inference(flattening,[],[f88]) ).

fof(f90,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) = X2
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ~ in(X4,X1)
              | ~ in(X4,X0) )
            & ( ( in(X4,X1)
                & in(X4,X0) )
              | ~ in(X4,X2) ) )
        | set_intersection2(X0,X1) != X2 ) ),
    inference(rectify,[],[f89]) ).

fof(f91,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ in(X3,X1)
            | ~ in(X3,X0)
            | ~ in(X3,X2) )
          & ( ( in(X3,X1)
              & in(X3,X0) )
            | in(X3,X2) ) )
     => ( ( ~ in(sK0(X0,X1,X2),X1)
          | ~ in(sK0(X0,X1,X2),X0)
          | ~ in(sK0(X0,X1,X2),X2) )
        & ( ( in(sK0(X0,X1,X2),X1)
            & in(sK0(X0,X1,X2),X0) )
          | in(sK0(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f92,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) = X2
        | ( ( ~ in(sK0(X0,X1,X2),X1)
            | ~ in(sK0(X0,X1,X2),X0)
            | ~ in(sK0(X0,X1,X2),X2) )
          & ( ( in(sK0(X0,X1,X2),X1)
              & in(sK0(X0,X1,X2),X0) )
            | in(sK0(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ~ in(X4,X1)
              | ~ in(X4,X0) )
            & ( ( in(X4,X1)
                & in(X4,X0) )
              | ~ in(X4,X2) ) )
        | set_intersection2(X0,X1) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f90,f91]) ).

fof(f93,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_rng(X0) = X1
            | ? [X2] :
                ( ( ! [X3] :
                      ( apply(X0,X3) != X2
                      | ~ in(X3,relation_dom(X0)) )
                  | ~ in(X2,X1) )
                & ( ? [X3] :
                      ( apply(X0,X3) = X2
                      & in(X3,relation_dom(X0)) )
                  | in(X2,X1) ) ) )
          & ( ! [X2] :
                ( ( in(X2,X1)
                  | ! [X3] :
                      ( apply(X0,X3) != X2
                      | ~ in(X3,relation_dom(X0)) ) )
                & ( ? [X3] :
                      ( apply(X0,X3) = X2
                      & in(X3,relation_dom(X0)) )
                  | ~ in(X2,X1) ) )
            | relation_rng(X0) != X1 ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f57]) ).

fof(f94,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_rng(X0) = X1
            | ? [X2] :
                ( ( ! [X3] :
                      ( apply(X0,X3) != X2
                      | ~ in(X3,relation_dom(X0)) )
                  | ~ in(X2,X1) )
                & ( ? [X4] :
                      ( apply(X0,X4) = X2
                      & in(X4,relation_dom(X0)) )
                  | in(X2,X1) ) ) )
          & ( ! [X5] :
                ( ( in(X5,X1)
                  | ! [X6] :
                      ( apply(X0,X6) != X5
                      | ~ in(X6,relation_dom(X0)) ) )
                & ( ? [X7] :
                      ( apply(X0,X7) = X5
                      & in(X7,relation_dom(X0)) )
                  | ~ in(X5,X1) ) )
            | relation_rng(X0) != X1 ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(rectify,[],[f93]) ).

fof(f95,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ! [X3] :
                ( apply(X0,X3) != X2
                | ~ in(X3,relation_dom(X0)) )
            | ~ in(X2,X1) )
          & ( ? [X4] :
                ( apply(X0,X4) = X2
                & in(X4,relation_dom(X0)) )
            | in(X2,X1) ) )
     => ( ( ! [X3] :
              ( apply(X0,X3) != sK1(X0,X1)
              | ~ in(X3,relation_dom(X0)) )
          | ~ in(sK1(X0,X1),X1) )
        & ( ? [X4] :
              ( apply(X0,X4) = sK1(X0,X1)
              & in(X4,relation_dom(X0)) )
          | in(sK1(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f96,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( apply(X0,X4) = sK1(X0,X1)
          & in(X4,relation_dom(X0)) )
     => ( sK1(X0,X1) = apply(X0,sK2(X0,X1))
        & in(sK2(X0,X1),relation_dom(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f97,plain,
    ! [X0,X5] :
      ( ? [X7] :
          ( apply(X0,X7) = X5
          & in(X7,relation_dom(X0)) )
     => ( apply(X0,sK3(X0,X5)) = X5
        & in(sK3(X0,X5),relation_dom(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f98,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_rng(X0) = X1
            | ( ( ! [X3] :
                    ( apply(X0,X3) != sK1(X0,X1)
                    | ~ in(X3,relation_dom(X0)) )
                | ~ in(sK1(X0,X1),X1) )
              & ( ( sK1(X0,X1) = apply(X0,sK2(X0,X1))
                  & in(sK2(X0,X1),relation_dom(X0)) )
                | in(sK1(X0,X1),X1) ) ) )
          & ( ! [X5] :
                ( ( in(X5,X1)
                  | ! [X6] :
                      ( apply(X0,X6) != X5
                      | ~ in(X6,relation_dom(X0)) ) )
                & ( ( apply(X0,sK3(X0,X5)) = X5
                    & in(sK3(X0,X5),relation_dom(X0)) )
                  | ~ in(X5,X1) ) )
            | relation_rng(X0) != X1 ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f94,f97,f96,f95]) ).

fof(f121,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,[],[f80]) ).

fof(f122,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,[],[f121]) ).

fof(f123,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,[],[f122]) ).

fof(f124,plain,
    ! [X1,X2] :
      ( ? [X3] :
          ( apply(X1,X3) != apply(X2,X3)
          & in(X3,relation_dom(X1)) )
     => ( apply(X1,sK15(X1,X2)) != apply(X2,sK15(X1,X2))
        & in(sK15(X1,X2),relation_dom(X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f125,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( ( relation_dom_restriction(X2,X0) = X1
              | ( apply(X1,sK15(X1,X2)) != apply(X2,sK15(X1,X2))
                & in(sK15(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,[sK15])],[f123,f124]) ).

fof(f126,plain,
    ( ? [X0,X1,X2] :
        ( ~ in(apply(X2,X1),relation_rng(relation_dom_restriction(X2,X0)))
        & in(X1,X0)
        & in(X1,relation_dom(X2))
        & function(X2)
        & relation(X2) )
   => ( ~ in(apply(sK18,sK17),relation_rng(relation_dom_restriction(sK18,sK16)))
      & in(sK17,sK16)
      & in(sK17,relation_dom(sK18))
      & function(sK18)
      & relation(sK18) ) ),
    introduced(choice_axiom,[]) ).

fof(f127,plain,
    ( ~ in(apply(sK18,sK17),relation_rng(relation_dom_restriction(sK18,sK16)))
    & in(sK17,sK16)
    & in(sK17,relation_dom(sK18))
    & function(sK18)
    & relation(sK18) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17,sK18])],[f85,f126]) ).

fof(f136,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X2)
      | ~ in(X4,X1)
      | ~ in(X4,X0)
      | set_intersection2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f92]) ).

fof(f142,plain,
    ! [X0,X1,X6,X5] :
      ( in(X5,X1)
      | apply(X0,X6) != X5
      | ~ in(X6,relation_dom(X0))
      | relation_rng(X0) != X1
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f98]) ).

fof(f146,plain,
    ! [X0,X1] :
      ( relation(relation_dom_restriction(X0,X1))
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f58]) ).

fof(f157,plain,
    ! [X0,X1] :
      ( function(relation_dom_restriction(X0,X1))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f64]) ).

fof(f193,plain,
    ! [X2,X0,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(cnf_transformation,[],[f125]) ).

fof(f198,plain,
    ! [X2,X0,X1] :
      ( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
      | ~ in(X1,X0)
      | ~ function(X2)
      | ~ relation(X2) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f199,plain,
    relation(sK18),
    inference(cnf_transformation,[],[f127]) ).

fof(f200,plain,
    function(sK18),
    inference(cnf_transformation,[],[f127]) ).

fof(f201,plain,
    in(sK17,relation_dom(sK18)),
    inference(cnf_transformation,[],[f127]) ).

fof(f202,plain,
    in(sK17,sK16),
    inference(cnf_transformation,[],[f127]) ).

fof(f203,plain,
    ~ in(apply(sK18,sK17),relation_rng(relation_dom_restriction(sK18,sK16))),
    inference(cnf_transformation,[],[f127]) ).

fof(f206,plain,
    ! [X0,X1,X4] :
      ( in(X4,set_intersection2(X0,X1))
      | ~ in(X4,X1)
      | ~ in(X4,X0) ),
    inference(equality_resolution,[],[f136]) ).

fof(f209,plain,
    ! [X0,X1,X6] :
      ( in(apply(X0,X6),X1)
      | ~ in(X6,relation_dom(X0))
      | relation_rng(X0) != X1
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f142]) ).

fof(f210,plain,
    ! [X0,X6] :
      ( in(apply(X0,X6),relation_rng(X0))
      | ~ in(X6,relation_dom(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f209]) ).

fof(f214,plain,
    ! [X2,X0] :
      ( set_intersection2(relation_dom(X2),X0) = relation_dom(relation_dom_restriction(X2,X0))
      | ~ function(X2)
      | ~ relation(X2)
      | ~ function(relation_dom_restriction(X2,X0))
      | ~ relation(relation_dom_restriction(X2,X0)) ),
    inference(equality_resolution,[],[f193]) ).

cnf(c_56,plain,
    ( ~ in(X0,X1)
    | ~ in(X0,X2)
    | in(X0,set_intersection2(X2,X1)) ),
    inference(cnf_transformation,[],[f206]) ).

cnf(c_62,plain,
    ( ~ in(X0,relation_dom(X1))
    | ~ function(X1)
    | ~ relation(X1)
    | in(apply(X1,X0),relation_rng(X1)) ),
    inference(cnf_transformation,[],[f210]) ).

cnf(c_65,plain,
    ( ~ relation(X0)
    | relation(relation_dom_restriction(X0,X1)) ),
    inference(cnf_transformation,[],[f146]) ).

cnf(c_75,plain,
    ( ~ function(X0)
    | ~ relation(X0)
    | function(relation_dom_restriction(X0,X1)) ),
    inference(cnf_transformation,[],[f157]) ).

cnf(c_115,plain,
    ( ~ function(relation_dom_restriction(X0,X1))
    | ~ relation(relation_dom_restriction(X0,X1))
    | ~ function(X0)
    | ~ relation(X0)
    | set_intersection2(relation_dom(X0),X1) = relation_dom(relation_dom_restriction(X0,X1)) ),
    inference(cnf_transformation,[],[f214]) ).

cnf(c_117,plain,
    ( ~ in(X0,X1)
    | ~ function(X2)
    | ~ relation(X2)
    | apply(relation_dom_restriction(X2,X1),X0) = apply(X2,X0) ),
    inference(cnf_transformation,[],[f198]) ).

cnf(c_118,negated_conjecture,
    ~ in(apply(sK18,sK17),relation_rng(relation_dom_restriction(sK18,sK16))),
    inference(cnf_transformation,[],[f203]) ).

cnf(c_119,negated_conjecture,
    in(sK17,sK16),
    inference(cnf_transformation,[],[f202]) ).

cnf(c_120,negated_conjecture,
    in(sK17,relation_dom(sK18)),
    inference(cnf_transformation,[],[f201]) ).

cnf(c_121,negated_conjecture,
    function(sK18),
    inference(cnf_transformation,[],[f200]) ).

cnf(c_122,negated_conjecture,
    relation(sK18),
    inference(cnf_transformation,[],[f199]) ).

cnf(c_162,plain,
    ( ~ function(X0)
    | ~ relation(X0)
    | set_intersection2(relation_dom(X0),X1) = relation_dom(relation_dom_restriction(X0,X1)) ),
    inference(global_subsumption_just,[status(thm)],[c_115,c_65,c_75,c_115]) ).

cnf(c_2549,plain,
    ( ~ relation(sK18)
    | set_intersection2(relation_dom(sK18),X0) = relation_dom(relation_dom_restriction(sK18,X0)) ),
    inference(superposition,[status(thm)],[c_121,c_162]) ).

cnf(c_2555,plain,
    set_intersection2(relation_dom(sK18),X0) = relation_dom(relation_dom_restriction(sK18,X0)),
    inference(forward_subsumption_resolution,[status(thm)],[c_2549,c_122]) ).

cnf(c_2745,plain,
    ( ~ in(X0,relation_dom(sK18))
    | ~ in(X0,X1)
    | in(X0,relation_dom(relation_dom_restriction(sK18,X1))) ),
    inference(superposition,[status(thm)],[c_2555,c_56]) ).

cnf(c_3581,plain,
    ( ~ function(X0)
    | ~ relation(X0)
    | apply(relation_dom_restriction(X0,sK16),sK17) = apply(X0,sK17) ),
    inference(superposition,[status(thm)],[c_119,c_117]) ).

cnf(c_4553,plain,
    ( ~ relation(sK18)
    | apply(relation_dom_restriction(sK18,sK16),sK17) = apply(sK18,sK17) ),
    inference(superposition,[status(thm)],[c_121,c_3581]) ).

cnf(c_4561,plain,
    apply(relation_dom_restriction(sK18,sK16),sK17) = apply(sK18,sK17),
    inference(forward_subsumption_resolution,[status(thm)],[c_4553,c_122]) ).

cnf(c_4630,plain,
    ( ~ in(sK17,relation_dom(relation_dom_restriction(sK18,sK16)))
    | ~ function(relation_dom_restriction(sK18,sK16))
    | ~ relation(relation_dom_restriction(sK18,sK16))
    | in(apply(sK18,sK17),relation_rng(relation_dom_restriction(sK18,sK16))) ),
    inference(superposition,[status(thm)],[c_4561,c_62]) ).

cnf(c_4631,plain,
    ( ~ in(sK17,relation_dom(relation_dom_restriction(sK18,sK16)))
    | ~ function(relation_dom_restriction(sK18,sK16))
    | ~ relation(relation_dom_restriction(sK18,sK16)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_4630,c_118]) ).

cnf(c_4798,plain,
    ( ~ in(sK17,relation_dom(sK18))
    | ~ function(relation_dom_restriction(sK18,sK16))
    | ~ relation(relation_dom_restriction(sK18,sK16))
    | ~ in(sK17,sK16) ),
    inference(superposition,[status(thm)],[c_2745,c_4631]) ).

cnf(c_4799,plain,
    ( ~ function(relation_dom_restriction(sK18,sK16))
    | ~ relation(relation_dom_restriction(sK18,sK16)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_4798,c_119,c_120]) ).

cnf(c_4808,plain,
    ( ~ relation(relation_dom_restriction(sK18,sK16))
    | ~ function(sK18)
    | ~ relation(sK18) ),
    inference(superposition,[status(thm)],[c_75,c_4799]) ).

cnf(c_4809,plain,
    ~ relation(relation_dom_restriction(sK18,sK16)),
    inference(forward_subsumption_resolution,[status(thm)],[c_4808,c_122,c_121]) ).

cnf(c_5033,plain,
    ~ relation(sK18),
    inference(superposition,[status(thm)],[c_65,c_4809]) ).

cnf(c_5034,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_5033,c_122]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : SEU039+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.10  % Command  : run_iprover %s %d THM
% 0.10/0.29  % Computer : n020.cluster.edu
% 0.10/0.29  % Model    : x86_64 x86_64
% 0.10/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29  % Memory   : 8042.1875MB
% 0.10/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29  % CPULimit : 300
% 0.10/0.29  % WCLimit  : 300
% 0.10/0.29  % DateTime : Thu Aug 24 01:32:01 EDT 2023
% 0.10/0.29  % CPUTime  : 
% 0.14/0.41  Running first-order theorem proving
% 0.14/0.41  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.69/1.09  % SZS status Started for theBenchmark.p
% 3.69/1.09  % SZS status Theorem for theBenchmark.p
% 3.69/1.09  
% 3.69/1.09  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.69/1.09  
% 3.69/1.09  ------  iProver source info
% 3.69/1.09  
% 3.69/1.09  git: date: 2023-05-31 18:12:56 +0000
% 3.69/1.09  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.69/1.09  git: non_committed_changes: false
% 3.69/1.09  git: last_make_outside_of_git: false
% 3.69/1.09  
% 3.69/1.09  ------ Parsing...
% 3.69/1.09  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.69/1.09  
% 3.69/1.09  ------ Preprocessing... sup_sim: 0  sf_s  rm: 5 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e 
% 3.69/1.09  
% 3.69/1.09  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.69/1.09  
% 3.69/1.09  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.69/1.09  ------ Proving...
% 3.69/1.09  ------ Problem Properties 
% 3.69/1.09  
% 3.69/1.09  
% 3.69/1.09  clauses                                 67
% 3.69/1.09  conjectures                             5
% 3.69/1.09  EPR                                     27
% 3.69/1.09  Horn                                    60
% 3.69/1.09  unary                                   29
% 3.69/1.09  binary                                  15
% 3.69/1.09  lits                                    149
% 3.69/1.09  lits eq                                 22
% 3.69/1.09  fd_pure                                 0
% 3.69/1.09  fd_pseudo                               0
% 3.69/1.09  fd_cond                                 1
% 3.69/1.09  fd_pseudo_cond                          9
% 3.69/1.09  AC symbols                              0
% 3.69/1.09  
% 3.69/1.09  ------ Schedule dynamic 5 is on 
% 3.69/1.09  
% 3.69/1.09  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.69/1.09  
% 3.69/1.09  
% 3.69/1.09  ------ 
% 3.69/1.09  Current options:
% 3.69/1.09  ------ 
% 3.69/1.09  
% 3.69/1.09  
% 3.69/1.09  
% 3.69/1.09  
% 3.69/1.09  ------ Proving...
% 3.69/1.09  
% 3.69/1.09  
% 3.69/1.09  % SZS status Theorem for theBenchmark.p
% 3.69/1.09  
% 3.69/1.09  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.69/1.09  
% 3.69/1.09  
%------------------------------------------------------------------------------