TSTP Solution File: SEU076+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SEU076+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n004.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 : Fri May  3 03:04:28 EDT 2024

% Result   : Theorem 61.61s 9.20s
% Output   : CNFRefutation 61.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   92 (  16 unt;   0 def)
%            Number of atoms       :  457 ( 102 equ)
%            Maximal formula atoms :   20 (   4 avg)
%            Number of connectives :  609 ( 244   ~; 238   |; 102   &)
%                                         (  11 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   3 con; 0-3 aty)
%            Number of variables   :  210 (   0 sgn 126   !;  32   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f5,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ! [X1,X2] :
          ( relation_image(X0,X1) = X2
        <=> ! [X3] :
              ( in(X3,X2)
            <=> ? [X4] :
                  ( apply(X0,X4) = X3
                  & in(X4,X1)
                  & in(X4,relation_dom(X0)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_funct_1) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

fof(f7,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/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).

fof(f26,conjecture,
    ! [X0,X1,X2] :
      ( ( function(X2)
        & relation(X2) )
     => ( ( one_to_one(X2)
          & subset(X0,relation_dom(X2))
          & subset(relation_image(X2,X0),relation_image(X2,X1)) )
       => subset(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t157_funct_1) ).

fof(f27,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ( function(X2)
          & relation(X2) )
       => ( ( one_to_one(X2)
            & subset(X0,relation_dom(X2))
            & subset(relation_image(X2,X0),relation_image(X2,X1)) )
         => subset(X0,X1) ) ),
    inference(negated_conjecture,[],[f26]) ).

fof(f44,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( relation_image(X0,X1) = X2
        <=> ! [X3] :
              ( in(X3,X2)
            <=> ? [X4] :
                  ( apply(X0,X4) = X3
                  & in(X4,X1)
                  & in(X4,relation_dom(X0)) ) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f45,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( relation_image(X0,X1) = X2
        <=> ! [X3] :
              ( in(X3,X2)
            <=> ? [X4] :
                  ( apply(X0,X4) = X3
                  & in(X4,X1)
                  & in(X4,relation_dom(X0)) ) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f44]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f47,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,[],[f7]) ).

fof(f48,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,[],[f47]) ).

fof(f53,plain,
    ? [X0,X1,X2] :
      ( ~ subset(X0,X1)
      & one_to_one(X2)
      & subset(X0,relation_dom(X2))
      & subset(relation_image(X2,X0),relation_image(X2,X1))
      & function(X2)
      & relation(X2) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f54,plain,
    ? [X0,X1,X2] :
      ( ~ subset(X0,X1)
      & one_to_one(X2)
      & subset(X0,relation_dom(X2))
      & subset(relation_image(X2,X0),relation_image(X2,X1))
      & function(X2)
      & relation(X2) ),
    inference(flattening,[],[f53]) ).

fof(f64,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( relation_image(X0,X1) = X2
            | ? [X3] :
                ( ( ! [X4] :
                      ( apply(X0,X4) != X3
                      | ~ in(X4,X1)
                      | ~ in(X4,relation_dom(X0)) )
                  | ~ in(X3,X2) )
                & ( ? [X4] :
                      ( apply(X0,X4) = X3
                      & in(X4,X1)
                      & in(X4,relation_dom(X0)) )
                  | in(X3,X2) ) ) )
          & ( ! [X3] :
                ( ( in(X3,X2)
                  | ! [X4] :
                      ( apply(X0,X4) != X3
                      | ~ in(X4,X1)
                      | ~ in(X4,relation_dom(X0)) ) )
                & ( ? [X4] :
                      ( apply(X0,X4) = X3
                      & in(X4,X1)
                      & in(X4,relation_dom(X0)) )
                  | ~ in(X3,X2) ) )
            | relation_image(X0,X1) != X2 ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f45]) ).

fof(f65,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( relation_image(X0,X1) = X2
            | ? [X3] :
                ( ( ! [X4] :
                      ( apply(X0,X4) != X3
                      | ~ in(X4,X1)
                      | ~ in(X4,relation_dom(X0)) )
                  | ~ in(X3,X2) )
                & ( ? [X5] :
                      ( apply(X0,X5) = X3
                      & in(X5,X1)
                      & in(X5,relation_dom(X0)) )
                  | in(X3,X2) ) ) )
          & ( ! [X6] :
                ( ( in(X6,X2)
                  | ! [X7] :
                      ( apply(X0,X7) != X6
                      | ~ in(X7,X1)
                      | ~ in(X7,relation_dom(X0)) ) )
                & ( ? [X8] :
                      ( apply(X0,X8) = X6
                      & in(X8,X1)
                      & in(X8,relation_dom(X0)) )
                  | ~ in(X6,X2) ) )
            | relation_image(X0,X1) != X2 ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(rectify,[],[f64]) ).

fof(f66,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ! [X4] :
                ( apply(X0,X4) != X3
                | ~ in(X4,X1)
                | ~ in(X4,relation_dom(X0)) )
            | ~ in(X3,X2) )
          & ( ? [X5] :
                ( apply(X0,X5) = X3
                & in(X5,X1)
                & in(X5,relation_dom(X0)) )
            | in(X3,X2) ) )
     => ( ( ! [X4] :
              ( apply(X0,X4) != sK0(X0,X1,X2)
              | ~ in(X4,X1)
              | ~ in(X4,relation_dom(X0)) )
          | ~ in(sK0(X0,X1,X2),X2) )
        & ( ? [X5] :
              ( apply(X0,X5) = sK0(X0,X1,X2)
              & in(X5,X1)
              & in(X5,relation_dom(X0)) )
          | in(sK0(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f67,plain,
    ! [X0,X1,X2] :
      ( ? [X5] :
          ( apply(X0,X5) = sK0(X0,X1,X2)
          & in(X5,X1)
          & in(X5,relation_dom(X0)) )
     => ( sK0(X0,X1,X2) = apply(X0,sK1(X0,X1,X2))
        & in(sK1(X0,X1,X2),X1)
        & in(sK1(X0,X1,X2),relation_dom(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f68,plain,
    ! [X0,X1,X6] :
      ( ? [X8] :
          ( apply(X0,X8) = X6
          & in(X8,X1)
          & in(X8,relation_dom(X0)) )
     => ( apply(X0,sK2(X0,X1,X6)) = X6
        & in(sK2(X0,X1,X6),X1)
        & in(sK2(X0,X1,X6),relation_dom(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f69,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( relation_image(X0,X1) = X2
            | ( ( ! [X4] :
                    ( apply(X0,X4) != sK0(X0,X1,X2)
                    | ~ in(X4,X1)
                    | ~ in(X4,relation_dom(X0)) )
                | ~ in(sK0(X0,X1,X2),X2) )
              & ( ( sK0(X0,X1,X2) = apply(X0,sK1(X0,X1,X2))
                  & in(sK1(X0,X1,X2),X1)
                  & in(sK1(X0,X1,X2),relation_dom(X0)) )
                | in(sK0(X0,X1,X2),X2) ) ) )
          & ( ! [X6] :
                ( ( in(X6,X2)
                  | ! [X7] :
                      ( apply(X0,X7) != X6
                      | ~ in(X7,X1)
                      | ~ in(X7,relation_dom(X0)) ) )
                & ( ( apply(X0,sK2(X0,X1,X6)) = X6
                    & in(sK2(X0,X1,X6),X1)
                    & in(sK2(X0,X1,X6),relation_dom(X0)) )
                  | ~ in(X6,X2) ) )
            | relation_image(X0,X1) != X2 ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f65,f68,f67,f66]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f46]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f70]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK3(X0,X1),X1)
        & in(sK3(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f73,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK3(X0,X1),X1)
          & in(sK3(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f71,f72]) ).

fof(f74,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,[],[f48]) ).

fof(f75,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,X4) != apply(X0,X3)
              | ~ in(X4,relation_dom(X0))
              | ~ in(X3,relation_dom(X0)) )
          | ~ one_to_one(X0) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(rectify,[],[f74]) ).

fof(f76,plain,
    ! [X0] :
      ( ? [X1,X2] :
          ( X1 != X2
          & apply(X0,X1) = apply(X0,X2)
          & in(X2,relation_dom(X0))
          & in(X1,relation_dom(X0)) )
     => ( sK4(X0) != sK5(X0)
        & apply(X0,sK4(X0)) = apply(X0,sK5(X0))
        & in(sK5(X0),relation_dom(X0))
        & in(sK4(X0),relation_dom(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f77,plain,
    ! [X0] :
      ( ( ( one_to_one(X0)
          | ( sK4(X0) != sK5(X0)
            & apply(X0,sK4(X0)) = apply(X0,sK5(X0))
            & in(sK5(X0),relation_dom(X0))
            & in(sK4(X0),relation_dom(X0)) ) )
        & ( ! [X3,X4] :
              ( X3 = X4
              | apply(X0,X4) != apply(X0,X3)
              | ~ 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,[sK4,sK5])],[f75,f76]) ).

fof(f100,plain,
    ( ? [X0,X1,X2] :
        ( ~ subset(X0,X1)
        & one_to_one(X2)
        & subset(X0,relation_dom(X2))
        & subset(relation_image(X2,X0),relation_image(X2,X1))
        & function(X2)
        & relation(X2) )
   => ( ~ subset(sK17,sK18)
      & one_to_one(sK19)
      & subset(sK17,relation_dom(sK19))
      & subset(relation_image(sK19,sK17),relation_image(sK19,sK18))
      & function(sK19)
      & relation(sK19) ) ),
    introduced(choice_axiom,[]) ).

fof(f101,plain,
    ( ~ subset(sK17,sK18)
    & one_to_one(sK19)
    & subset(sK17,relation_dom(sK19))
    & subset(relation_image(sK19,sK17),relation_image(sK19,sK18))
    & function(sK19)
    & relation(sK19) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18,sK19])],[f54,f100]) ).

fof(f109,plain,
    ! [X2,X0,X1,X6] :
      ( in(sK2(X0,X1,X6),relation_dom(X0))
      | ~ in(X6,X2)
      | relation_image(X0,X1) != X2
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f69]) ).

fof(f110,plain,
    ! [X2,X0,X1,X6] :
      ( in(sK2(X0,X1,X6),X1)
      | ~ in(X6,X2)
      | relation_image(X0,X1) != X2
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f69]) ).

fof(f111,plain,
    ! [X2,X0,X1,X6] :
      ( apply(X0,sK2(X0,X1,X6)) = X6
      | ~ in(X6,X2)
      | relation_image(X0,X1) != X2
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f69]) ).

fof(f112,plain,
    ! [X2,X0,X1,X6,X7] :
      ( in(X6,X2)
      | apply(X0,X7) != X6
      | ~ in(X7,X1)
      | ~ in(X7,relation_dom(X0))
      | relation_image(X0,X1) != X2
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f69]) ).

fof(f117,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | ~ in(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f73]) ).

fof(f118,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sK3(X0,X1),X0) ),
    inference(cnf_transformation,[],[f73]) ).

fof(f119,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ in(sK3(X0,X1),X1) ),
    inference(cnf_transformation,[],[f73]) ).

fof(f120,plain,
    ! [X3,X0,X4] :
      ( X3 = X4
      | apply(X0,X4) != apply(X0,X3)
      | ~ in(X4,relation_dom(X0))
      | ~ in(X3,relation_dom(X0))
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f155,plain,
    relation(sK19),
    inference(cnf_transformation,[],[f101]) ).

fof(f156,plain,
    function(sK19),
    inference(cnf_transformation,[],[f101]) ).

fof(f157,plain,
    subset(relation_image(sK19,sK17),relation_image(sK19,sK18)),
    inference(cnf_transformation,[],[f101]) ).

fof(f158,plain,
    subset(sK17,relation_dom(sK19)),
    inference(cnf_transformation,[],[f101]) ).

fof(f159,plain,
    one_to_one(sK19),
    inference(cnf_transformation,[],[f101]) ).

fof(f160,plain,
    ~ subset(sK17,sK18),
    inference(cnf_transformation,[],[f101]) ).

fof(f170,plain,
    ! [X2,X0,X1,X7] :
      ( in(apply(X0,X7),X2)
      | ~ in(X7,X1)
      | ~ in(X7,relation_dom(X0))
      | relation_image(X0,X1) != X2
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f112]) ).

fof(f171,plain,
    ! [X0,X1,X7] :
      ( in(apply(X0,X7),relation_image(X0,X1))
      | ~ in(X7,X1)
      | ~ in(X7,relation_dom(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f170]) ).

fof(f172,plain,
    ! [X0,X1,X6] :
      ( apply(X0,sK2(X0,X1,X6)) = X6
      | ~ in(X6,relation_image(X0,X1))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f111]) ).

fof(f173,plain,
    ! [X0,X1,X6] :
      ( in(sK2(X0,X1,X6),X1)
      | ~ in(X6,relation_image(X0,X1))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f110]) ).

fof(f174,plain,
    ! [X0,X1,X6] :
      ( in(sK2(X0,X1,X6),relation_dom(X0))
      | ~ in(X6,relation_image(X0,X1))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f109]) ).

cnf(c_57,plain,
    ( ~ in(X0,relation_dom(X1))
    | ~ in(X0,X2)
    | ~ function(X1)
    | ~ relation(X1)
    | in(apply(X1,X0),relation_image(X1,X2)) ),
    inference(cnf_transformation,[],[f171]) ).

cnf(c_58,plain,
    ( ~ in(X0,relation_image(X1,X2))
    | ~ function(X1)
    | ~ relation(X1)
    | apply(X1,sK2(X1,X2,X0)) = X0 ),
    inference(cnf_transformation,[],[f172]) ).

cnf(c_59,plain,
    ( ~ in(X0,relation_image(X1,X2))
    | ~ function(X1)
    | ~ relation(X1)
    | in(sK2(X1,X2,X0),X2) ),
    inference(cnf_transformation,[],[f173]) ).

cnf(c_60,plain,
    ( ~ in(X0,relation_image(X1,X2))
    | ~ function(X1)
    | ~ relation(X1)
    | in(sK2(X1,X2,X0),relation_dom(X1)) ),
    inference(cnf_transformation,[],[f174]) ).

cnf(c_61,plain,
    ( ~ in(sK3(X0,X1),X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f119]) ).

cnf(c_62,plain,
    ( in(sK3(X0,X1),X0)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f118]) ).

cnf(c_63,plain,
    ( ~ in(X0,X1)
    | ~ subset(X1,X2)
    | in(X0,X2) ),
    inference(cnf_transformation,[],[f117]) ).

cnf(c_68,plain,
    ( apply(X0,X1) != apply(X0,X2)
    | ~ in(X1,relation_dom(X0))
    | ~ in(X2,relation_dom(X0))
    | ~ function(X0)
    | ~ relation(X0)
    | ~ one_to_one(X0)
    | X1 = X2 ),
    inference(cnf_transformation,[],[f120]) ).

cnf(c_99,negated_conjecture,
    ~ subset(sK17,sK18),
    inference(cnf_transformation,[],[f160]) ).

cnf(c_100,negated_conjecture,
    one_to_one(sK19),
    inference(cnf_transformation,[],[f159]) ).

cnf(c_101,negated_conjecture,
    subset(sK17,relation_dom(sK19)),
    inference(cnf_transformation,[],[f158]) ).

cnf(c_102,negated_conjecture,
    subset(relation_image(sK19,sK17),relation_image(sK19,sK18)),
    inference(cnf_transformation,[],[f157]) ).

cnf(c_103,negated_conjecture,
    function(sK19),
    inference(cnf_transformation,[],[f156]) ).

cnf(c_104,negated_conjecture,
    relation(sK19),
    inference(cnf_transformation,[],[f155]) ).

cnf(c_168,plain,
    X0 = X0,
    theory(equality) ).

cnf(c_170,plain,
    ( X0 != X1
    | X2 != X1
    | X2 = X0 ),
    theory(equality) ).

cnf(c_171,plain,
    ( X0 != X1
    | X2 != X3
    | ~ in(X1,X3)
    | in(X0,X2) ),
    theory(equality) ).

cnf(c_189,plain,
    ( in(sK3(sK17,sK18),sK17)
    | subset(sK17,sK18) ),
    inference(instantiation,[status(thm)],[c_62]) ).

cnf(c_229,plain,
    ( ~ in(sK3(sK17,sK18),sK17)
    | ~ subset(sK17,X0)
    | in(sK3(sK17,sK18),X0) ),
    inference(instantiation,[status(thm)],[c_63]) ).

cnf(c_232,plain,
    ( ~ in(sK3(sK17,sK18),relation_dom(X0))
    | ~ in(sK3(sK17,sK18),sK17)
    | ~ function(X0)
    | ~ relation(X0)
    | in(apply(X0,sK3(sK17,sK18)),relation_image(X0,sK17)) ),
    inference(instantiation,[status(thm)],[c_57]) ).

cnf(c_247,plain,
    sK18 = sK18,
    inference(instantiation,[status(thm)],[c_168]) ).

cnf(c_419,plain,
    ( ~ in(sK3(sK17,sK18),sK17)
    | ~ subset(sK17,relation_dom(sK19))
    | in(sK3(sK17,sK18),relation_dom(sK19)) ),
    inference(instantiation,[status(thm)],[c_229]) ).

cnf(c_920,plain,
    ( ~ in(sK3(sK17,sK18),relation_dom(sK19))
    | ~ in(sK3(sK17,sK18),sK17)
    | ~ function(sK19)
    | ~ relation(sK19)
    | in(apply(sK19,sK3(sK17,sK18)),relation_image(sK19,sK17)) ),
    inference(instantiation,[status(thm)],[c_232]) ).

cnf(c_1186,plain,
    ( apply(X0,X1) != apply(X0,sK3(sK17,sK18))
    | ~ in(sK3(sK17,sK18),relation_dom(X0))
    | ~ in(X1,relation_dom(X0))
    | ~ function(X0)
    | ~ relation(X0)
    | ~ one_to_one(X0)
    | X1 = sK3(sK17,sK18) ),
    inference(instantiation,[status(thm)],[c_68]) ).

cnf(c_1307,plain,
    ( ~ in(X0,relation_image(X1,X2))
    | ~ subset(relation_image(X1,X2),X3)
    | in(X0,X3) ),
    inference(instantiation,[status(thm)],[c_63]) ).

cnf(c_3108,plain,
    sK3(sK17,sK18) = sK3(sK17,sK18),
    inference(instantiation,[status(thm)],[c_168]) ).

cnf(c_3306,plain,
    ( sK3(sK17,sK18) != X0
    | X1 != X0
    | sK3(sK17,sK18) = X1 ),
    inference(instantiation,[status(thm)],[c_170]) ).

cnf(c_3509,plain,
    ( ~ in(sK3(X0,sK18),sK18)
    | subset(X0,sK18) ),
    inference(instantiation,[status(thm)],[c_61]) ).

cnf(c_4737,plain,
    ( ~ in(apply(sK19,sK3(sK17,sK18)),relation_image(sK19,sK17))
    | ~ subset(relation_image(sK19,sK17),X0)
    | in(apply(sK19,sK3(sK17,sK18)),X0) ),
    inference(instantiation,[status(thm)],[c_1307]) ).

cnf(c_4745,plain,
    ( apply(sK19,X0) != apply(sK19,sK3(sK17,sK18))
    | ~ in(sK3(sK17,sK18),relation_dom(sK19))
    | ~ in(X0,relation_dom(sK19))
    | ~ function(sK19)
    | ~ relation(sK19)
    | ~ one_to_one(sK19)
    | X0 = sK3(sK17,sK18) ),
    inference(instantiation,[status(thm)],[c_1186]) ).

cnf(c_8089,plain,
    ( apply(sK19,sK2(sK19,X0,apply(sK19,sK3(sK17,sK18)))) != apply(sK19,sK3(sK17,sK18))
    | ~ in(sK2(sK19,X0,apply(sK19,sK3(sK17,sK18))),relation_dom(sK19))
    | ~ in(sK3(sK17,sK18),relation_dom(sK19))
    | ~ function(sK19)
    | ~ relation(sK19)
    | ~ one_to_one(sK19)
    | sK2(sK19,X0,apply(sK19,sK3(sK17,sK18))) = sK3(sK17,sK18) ),
    inference(instantiation,[status(thm)],[c_4745]) ).

cnf(c_8090,plain,
    ( ~ in(apply(sK19,sK3(sK17,sK18)),relation_image(sK19,X0))
    | ~ function(sK19)
    | ~ relation(sK19)
    | apply(sK19,sK2(sK19,X0,apply(sK19,sK3(sK17,sK18)))) = apply(sK19,sK3(sK17,sK18)) ),
    inference(instantiation,[status(thm)],[c_58]) ).

cnf(c_8874,plain,
    ( ~ in(apply(sK19,sK3(sK17,sK18)),relation_image(sK19,sK17))
    | ~ subset(relation_image(sK19,sK17),relation_image(sK19,sK18))
    | in(apply(sK19,sK3(sK17,sK18)),relation_image(sK19,sK18)) ),
    inference(instantiation,[status(thm)],[c_4737]) ).

cnf(c_9580,plain,
    ( ~ in(sK3(sK17,sK18),sK18)
    | subset(sK17,sK18) ),
    inference(instantiation,[status(thm)],[c_3509]) ).

cnf(c_10063,plain,
    ( sK3(sK17,sK18) != sK3(sK17,sK18)
    | X0 != sK3(sK17,sK18)
    | sK3(sK17,sK18) = X0 ),
    inference(instantiation,[status(thm)],[c_3306]) ).

cnf(c_12959,plain,
    ( ~ in(apply(sK19,sK3(sK17,sK18)),relation_image(sK19,sK18))
    | ~ function(sK19)
    | ~ relation(sK19)
    | in(sK2(sK19,sK18,apply(sK19,sK3(sK17,sK18))),relation_dom(sK19)) ),
    inference(instantiation,[status(thm)],[c_60]) ).

cnf(c_12960,plain,
    ( ~ in(apply(sK19,sK3(sK17,sK18)),relation_image(sK19,sK18))
    | ~ function(sK19)
    | ~ relation(sK19)
    | in(sK2(sK19,sK18,apply(sK19,sK3(sK17,sK18))),sK18) ),
    inference(instantiation,[status(thm)],[c_59]) ).

cnf(c_13673,plain,
    ( ~ in(apply(sK19,sK3(sK17,sK18)),relation_image(sK19,sK18))
    | ~ function(sK19)
    | ~ relation(sK19)
    | apply(sK19,sK2(sK19,sK18,apply(sK19,sK3(sK17,sK18)))) = apply(sK19,sK3(sK17,sK18)) ),
    inference(instantiation,[status(thm)],[c_8090]) ).

cnf(c_20334,plain,
    ( apply(sK19,sK2(sK19,sK18,apply(sK19,sK3(sK17,sK18)))) != apply(sK19,sK3(sK17,sK18))
    | ~ in(sK2(sK19,sK18,apply(sK19,sK3(sK17,sK18))),relation_dom(sK19))
    | ~ in(sK3(sK17,sK18),relation_dom(sK19))
    | ~ function(sK19)
    | ~ relation(sK19)
    | ~ one_to_one(sK19)
    | sK2(sK19,sK18,apply(sK19,sK3(sK17,sK18))) = sK3(sK17,sK18) ),
    inference(instantiation,[status(thm)],[c_8089]) ).

cnf(c_29943,plain,
    ( sK2(sK19,sK18,apply(sK19,sK3(sK17,sK18))) != sK3(sK17,sK18)
    | sK3(sK17,sK18) != sK3(sK17,sK18)
    | sK3(sK17,sK18) = sK2(sK19,sK18,apply(sK19,sK3(sK17,sK18))) ),
    inference(instantiation,[status(thm)],[c_10063]) ).

cnf(c_42916,plain,
    ( X0 != X1
    | X2 != sK18
    | ~ in(X1,sK18)
    | in(X0,X2) ),
    inference(instantiation,[status(thm)],[c_171]) ).

cnf(c_52224,plain,
    ( X0 != X1
    | sK18 != sK18
    | ~ in(X1,sK18)
    | in(X0,sK18) ),
    inference(instantiation,[status(thm)],[c_42916]) ).

cnf(c_54024,plain,
    ( sK3(sK17,sK18) != X0
    | sK18 != sK18
    | ~ in(X0,sK18)
    | in(sK3(sK17,sK18),sK18) ),
    inference(instantiation,[status(thm)],[c_52224]) ).

cnf(c_59545,plain,
    ( sK3(sK17,sK18) != sK2(sK19,sK18,apply(sK19,sK3(sK17,sK18)))
    | sK18 != sK18
    | ~ in(sK2(sK19,sK18,apply(sK19,sK3(sK17,sK18))),sK18)
    | in(sK3(sK17,sK18),sK18) ),
    inference(instantiation,[status(thm)],[c_54024]) ).

cnf(c_59546,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_59545,c_29943,c_20334,c_13673,c_12959,c_12960,c_9580,c_8874,c_3108,c_920,c_419,c_247,c_189,c_102,c_99,c_101,c_100,c_103,c_104]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SEU076+1 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.12  % Command  : run_iprover %s %d THM
% 0.11/0.32  % Computer : n004.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.33  % DateTime : Thu May  2 17:29:33 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 0.18/0.44  Running first-order theorem proving
% 0.18/0.44  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 61.61/9.20  % SZS status Started for theBenchmark.p
% 61.61/9.20  % SZS status Theorem for theBenchmark.p
% 61.61/9.20  
% 61.61/9.20  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 61.61/9.20  
% 61.61/9.20  ------  iProver source info
% 61.61/9.20  
% 61.61/9.20  git: date: 2024-05-02 19:28:25 +0000
% 61.61/9.20  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 61.61/9.20  git: non_committed_changes: false
% 61.61/9.20  
% 61.61/9.20  ------ Parsing...
% 61.61/9.20  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 61.61/9.20  
% 61.61/9.20  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 1 0s  sf_e 
% 61.61/9.20  
% 61.61/9.20  ------ Preprocessing...
% 61.61/9.20  
% 61.61/9.20  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 61.61/9.20  ------ Proving...
% 61.61/9.20  ------ Problem Properties 
% 61.61/9.20  
% 61.61/9.20  
% 61.61/9.20  clauses                                 62
% 61.61/9.20  conjectures                             6
% 61.61/9.20  EPR                                     32
% 61.61/9.20  Horn                                    53
% 61.61/9.20  unary                                   28
% 61.61/9.20  binary                                  15
% 61.61/9.20  lits                                    138
% 61.61/9.20  lits eq                                 13
% 61.61/9.20  fd_pure                                 0
% 61.61/9.20  fd_pseudo                               0
% 61.61/9.20  fd_cond                                 1
% 61.61/9.20  fd_pseudo_cond                          6
% 61.61/9.20  AC symbols                              0
% 61.61/9.20  
% 61.61/9.20  ------ Input Options Time Limit: Unbounded
% 61.61/9.20  
% 61.61/9.20  
% 61.61/9.20  ------ 
% 61.61/9.20  Current options:
% 61.61/9.20  ------ 
% 61.61/9.20  
% 61.61/9.20  
% 61.61/9.20  
% 61.61/9.20  
% 61.61/9.20  ------ Proving...
% 61.61/9.20  
% 61.61/9.20  
% 61.61/9.20  % SZS status Theorem for theBenchmark.p
% 61.61/9.20  
% 61.61/9.20  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 61.61/9.20  
% 61.61/9.21  
%------------------------------------------------------------------------------