TSTP Solution File: SEU081+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SEU081+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n002.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 03:04:29 EDT 2024

% Result   : Theorem 61.81s 9.27s
% Output   : CNFRefutation 61.81s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   20
% Syntax   : Number of formulae    :  124 (  22 unt;   0 def)
%            Number of atoms       :  482 ( 159 equ)
%            Maximal formula atoms :   20 (   3 avg)
%            Number of connectives :  619 ( 261   ~; 267   |;  69   &)
%                                         (   9 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   2 con; 0-3 aty)
%            Number of variables   :  226 (   4 sgn 128   !;  24   ?)

% 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(f7,axiom,
    ! [X0] :
    ? [X1] : element(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).

fof(f11,axiom,
    ! [X0] :
      ( function(identity_relation(X0))
      & relation(identity_relation(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).

fof(f26,conjecture,
    ! [X0,X1] :
      ( element(X1,powerset(X0))
     => relation_image(identity_relation(X0),X1) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t162_funct_1) ).

fof(f27,negated_conjecture,
    ~ ! [X0,X1] :
        ( element(X1,powerset(X0))
       => relation_image(identity_relation(X0),X1) = X1 ),
    inference(negated_conjecture,[],[f26]) ).

fof(f29,axiom,
    ! [X0,X1] :
      ( element(X0,X1)
     => ( in(X0,X1)
        | empty(X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).

fof(f30,axiom,
    ! [X0,X1] :
      ( ( function(X1)
        & relation(X1) )
     => ( identity_relation(X0) = X1
      <=> ( ! [X2] :
              ( in(X2,X0)
             => apply(X1,X2) = X2 )
          & relation_dom(X1) = X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).

fof(f32,axiom,
    ! [X0,X1,X2] :
      ( ( element(X1,powerset(X2))
        & in(X0,X1) )
     => element(X0,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).

fof(f33,axiom,
    ! [X0,X1,X2] :
      ~ ( empty(X2)
        & element(X1,powerset(X2))
        & in(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).

fof(f35,axiom,
    ! [X0,X1] :
      ~ ( empty(X1)
        & in(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).

fof(f48,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(f49,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,[],[f48]) ).

fof(f54,plain,
    ? [X0,X1] :
      ( relation_image(identity_relation(X0),X1) != X1
      & element(X1,powerset(X0)) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(ennf_transformation,[],[f29]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(flattening,[],[f56]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( ( identity_relation(X0) = X1
      <=> ( ! [X2] :
              ( apply(X1,X2) = X2
              | ~ in(X2,X0) )
          & relation_dom(X1) = X0 ) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( ( identity_relation(X0) = X1
      <=> ( ! [X2] :
              ( apply(X1,X2) = X2
              | ~ in(X2,X0) )
          & relation_dom(X1) = X0 ) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(flattening,[],[f58]) ).

fof(f61,plain,
    ! [X0,X1,X2] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f62,plain,
    ! [X0,X1,X2] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(flattening,[],[f61]) ).

fof(f63,plain,
    ! [X0,X1,X2] :
      ( ~ empty(X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f65,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f35]) ).

fof(f67,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,[],[f49]) ).

fof(f68,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,[],[f67]) ).

fof(f69,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(f70,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(f71,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(f72,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])],[f68,f71,f70,f69]) ).

fof(f73,plain,
    ! [X0] :
      ( ? [X1] : element(X1,X0)
     => element(sK3(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f74,plain,
    ! [X0] : element(sK3(X0),X0),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f7,f73]) ).

fof(f95,plain,
    ( ? [X0,X1] :
        ( relation_image(identity_relation(X0),X1) != X1
        & element(X1,powerset(X0)) )
   => ( sK15 != relation_image(identity_relation(sK14),sK15)
      & element(sK15,powerset(sK14)) ) ),
    introduced(choice_axiom,[]) ).

fof(f96,plain,
    ( sK15 != relation_image(identity_relation(sK14),sK15)
    & element(sK15,powerset(sK14)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f54,f95]) ).

fof(f97,plain,
    ! [X0,X1] :
      ( ( ( identity_relation(X0) = X1
          | ? [X2] :
              ( apply(X1,X2) != X2
              & in(X2,X0) )
          | relation_dom(X1) != X0 )
        & ( ( ! [X2] :
                ( apply(X1,X2) = X2
                | ~ in(X2,X0) )
            & relation_dom(X1) = X0 )
          | identity_relation(X0) != X1 ) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(nnf_transformation,[],[f59]) ).

fof(f98,plain,
    ! [X0,X1] :
      ( ( ( identity_relation(X0) = X1
          | ? [X2] :
              ( apply(X1,X2) != X2
              & in(X2,X0) )
          | relation_dom(X1) != X0 )
        & ( ( ! [X2] :
                ( apply(X1,X2) = X2
                | ~ in(X2,X0) )
            & relation_dom(X1) = X0 )
          | identity_relation(X0) != X1 ) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(flattening,[],[f97]) ).

fof(f99,plain,
    ! [X0,X1] :
      ( ( ( identity_relation(X0) = X1
          | ? [X2] :
              ( apply(X1,X2) != X2
              & in(X2,X0) )
          | relation_dom(X1) != X0 )
        & ( ( ! [X3] :
                ( apply(X1,X3) = X3
                | ~ in(X3,X0) )
            & relation_dom(X1) = X0 )
          | identity_relation(X0) != X1 ) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(rectify,[],[f98]) ).

fof(f100,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( apply(X1,X2) != X2
          & in(X2,X0) )
     => ( sK16(X0,X1) != apply(X1,sK16(X0,X1))
        & in(sK16(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f101,plain,
    ! [X0,X1] :
      ( ( ( identity_relation(X0) = X1
          | ( sK16(X0,X1) != apply(X1,sK16(X0,X1))
            & in(sK16(X0,X1),X0) )
          | relation_dom(X1) != X0 )
        & ( ( ! [X3] :
                ( apply(X1,X3) = X3
                | ~ in(X3,X0) )
            & relation_dom(X1) = X0 )
          | identity_relation(X0) != X1 ) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f99,f100]) ).

fof(f112,plain,
    ! [X2,X0,X1] :
      ( relation_image(X0,X1) = X2
      | in(sK1(X0,X1,X2),X1)
      | in(sK0(X0,X1,X2),X2)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f113,plain,
    ! [X2,X0,X1] :
      ( relation_image(X0,X1) = X2
      | sK0(X0,X1,X2) = apply(X0,sK1(X0,X1,X2))
      | in(sK0(X0,X1,X2),X2)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f114,plain,
    ! [X2,X0,X1,X4] :
      ( relation_image(X0,X1) = X2
      | apply(X0,X4) != sK0(X0,X1,X2)
      | ~ in(X4,X1)
      | ~ in(X4,relation_dom(X0))
      | ~ in(sK0(X0,X1,X2),X2)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f116,plain,
    ! [X0] : element(sK3(X0),X0),
    inference(cnf_transformation,[],[f74]) ).

fof(f121,plain,
    ! [X0] : relation(identity_relation(X0)),
    inference(cnf_transformation,[],[f11]) ).

fof(f122,plain,
    ! [X0] : function(identity_relation(X0)),
    inference(cnf_transformation,[],[f11]) ).

fof(f147,plain,
    element(sK15,powerset(sK14)),
    inference(cnf_transformation,[],[f96]) ).

fof(f148,plain,
    sK15 != relation_image(identity_relation(sK14),sK15),
    inference(cnf_transformation,[],[f96]) ).

fof(f150,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(cnf_transformation,[],[f57]) ).

fof(f151,plain,
    ! [X0,X1] :
      ( relation_dom(X1) = X0
      | identity_relation(X0) != X1
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f101]) ).

fof(f152,plain,
    ! [X3,X0,X1] :
      ( apply(X1,X3) = X3
      | ~ in(X3,X0)
      | identity_relation(X0) != X1
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f101]) ).

fof(f156,plain,
    ! [X2,X0,X1] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f157,plain,
    ! [X2,X0,X1] :
      ( ~ empty(X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f159,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f168,plain,
    ! [X3,X0] :
      ( apply(identity_relation(X0),X3) = X3
      | ~ in(X3,X0)
      | ~ function(identity_relation(X0))
      | ~ relation(identity_relation(X0)) ),
    inference(equality_resolution,[],[f152]) ).

fof(f169,plain,
    ! [X0] :
      ( relation_dom(identity_relation(X0)) = X0
      | ~ function(identity_relation(X0))
      | ~ relation(identity_relation(X0)) ),
    inference(equality_resolution,[],[f151]) ).

cnf(c_52,plain,
    ( sK0(X0,X1,X2) != apply(X0,X3)
    | ~ in(sK0(X0,X1,X2),X2)
    | ~ in(X3,relation_dom(X0))
    | ~ in(X3,X1)
    | ~ function(X0)
    | ~ relation(X0)
    | relation_image(X0,X1) = X2 ),
    inference(cnf_transformation,[],[f114]) ).

cnf(c_53,plain,
    ( ~ function(X0)
    | ~ relation(X0)
    | apply(X0,sK1(X0,X1,X2)) = sK0(X0,X1,X2)
    | relation_image(X0,X1) = X2
    | in(sK0(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f113]) ).

cnf(c_54,plain,
    ( ~ function(X0)
    | ~ relation(X0)
    | relation_image(X0,X1) = X2
    | in(sK0(X0,X1,X2),X2)
    | in(sK1(X0,X1,X2),X1) ),
    inference(cnf_transformation,[],[f112]) ).

cnf(c_61,plain,
    element(sK3(X0),X0),
    inference(cnf_transformation,[],[f116]) ).

cnf(c_66,plain,
    function(identity_relation(X0)),
    inference(cnf_transformation,[],[f122]) ).

cnf(c_67,plain,
    relation(identity_relation(X0)),
    inference(cnf_transformation,[],[f121]) ).

cnf(c_92,negated_conjecture,
    relation_image(identity_relation(sK14),sK15) != sK15,
    inference(cnf_transformation,[],[f148]) ).

cnf(c_93,negated_conjecture,
    element(sK15,powerset(sK14)),
    inference(cnf_transformation,[],[f147]) ).

cnf(c_95,plain,
    ( ~ element(X0,X1)
    | in(X0,X1)
    | empty(X1) ),
    inference(cnf_transformation,[],[f150]) ).

cnf(c_98,plain,
    ( ~ in(X0,X1)
    | ~ function(identity_relation(X1))
    | ~ relation(identity_relation(X1))
    | apply(identity_relation(X1),X0) = X0 ),
    inference(cnf_transformation,[],[f168]) ).

cnf(c_99,plain,
    ( ~ function(identity_relation(X0))
    | ~ relation(identity_relation(X0))
    | relation_dom(identity_relation(X0)) = X0 ),
    inference(cnf_transformation,[],[f169]) ).

cnf(c_101,plain,
    ( ~ element(X0,powerset(X1))
    | ~ in(X2,X0)
    | element(X2,X1) ),
    inference(cnf_transformation,[],[f156]) ).

cnf(c_102,plain,
    ( ~ element(X0,powerset(X1))
    | ~ in(X2,X0)
    | ~ empty(X1) ),
    inference(cnf_transformation,[],[f157]) ).

cnf(c_104,plain,
    ( ~ in(X0,X1)
    | ~ empty(X1) ),
    inference(cnf_transformation,[],[f159]) ).

cnf(c_130,plain,
    relation_dom(identity_relation(X0)) = X0,
    inference(global_subsumption_just,[status(thm)],[c_99,c_67,c_66,c_99]) ).

cnf(c_161,plain,
    X0 = X0,
    theory(equality) ).

cnf(c_163,plain,
    ( X0 != X1
    | X2 != X1
    | X2 = X0 ),
    theory(equality) ).

cnf(c_164,plain,
    ( X0 != X1
    | X2 != X3
    | ~ in(X1,X3)
    | in(X0,X2) ),
    theory(equality) ).

cnf(c_172,plain,
    ( X0 != X1
    | X2 != X3
    | ~ element(X1,X3)
    | element(X0,X2) ),
    theory(equality) ).

cnf(c_173,plain,
    ( X0 != X1
    | powerset(X0) = powerset(X1) ),
    theory(equality) ).

cnf(c_198,plain,
    ( X0 != sK15
    | X1 != powerset(sK14)
    | ~ element(sK15,powerset(sK14))
    | element(X0,X1) ),
    inference(instantiation,[status(thm)],[c_172]) ).

cnf(c_204,plain,
    ( ~ function(identity_relation(sK14))
    | ~ relation(identity_relation(sK14))
    | apply(identity_relation(sK14),sK1(identity_relation(sK14),sK15,sK15)) = sK0(identity_relation(sK14),sK15,sK15)
    | relation_image(identity_relation(sK14),sK15) = sK15
    | in(sK0(identity_relation(sK14),sK15,sK15),sK15) ),
    inference(instantiation,[status(thm)],[c_53]) ).

cnf(c_223,plain,
    ( ~ element(X0,sK15)
    | in(X0,sK15)
    | empty(sK15) ),
    inference(instantiation,[status(thm)],[c_95]) ).

cnf(c_233,plain,
    relation(identity_relation(sK14)),
    inference(instantiation,[status(thm)],[c_67]) ).

cnf(c_263,plain,
    ( X0 != powerset(sK14)
    | sK15 != sK15
    | ~ element(sK15,powerset(sK14))
    | element(sK15,X0) ),
    inference(instantiation,[status(thm)],[c_198]) ).

cnf(c_264,plain,
    sK15 = sK15,
    inference(instantiation,[status(thm)],[c_161]) ).

cnf(c_547,plain,
    function(identity_relation(sK14)),
    inference(instantiation,[status(thm)],[c_66]) ).

cnf(c_620,plain,
    ( X0 != sK14
    | powerset(X0) = powerset(sK14) ),
    inference(instantiation,[status(thm)],[c_173]) ).

cnf(c_1120,plain,
    ( ~ element(sK3(sK15),sK15)
    | in(sK3(sK15),sK15)
    | empty(sK15) ),
    inference(instantiation,[status(thm)],[c_223]) ).

cnf(c_1121,plain,
    element(sK3(sK15),sK15),
    inference(instantiation,[status(thm)],[c_61]) ).

cnf(c_1669,plain,
    ( ~ in(sK0(identity_relation(sK14),sK15,sK15),sK15)
    | ~ empty(sK15) ),
    inference(instantiation,[status(thm)],[c_104]) ).

cnf(c_1673,plain,
    ( sK0(X0,sK15,X1) != apply(X0,sK0(identity_relation(sK14),sK15,sK15))
    | ~ in(sK0(identity_relation(sK14),sK15,sK15),relation_dom(X0))
    | ~ in(sK0(identity_relation(sK14),sK15,sK15),sK15)
    | ~ in(sK0(X0,sK15,X1),X1)
    | ~ function(X0)
    | ~ relation(X0)
    | relation_image(X0,sK15) = X1 ),
    inference(instantiation,[status(thm)],[c_52]) ).

cnf(c_1677,plain,
    ( ~ in(sK0(identity_relation(sK14),sK15,sK15),sK15)
    | ~ element(sK15,powerset(X0))
    | element(sK0(identity_relation(sK14),sK15,sK15),X0) ),
    inference(instantiation,[status(thm)],[c_101]) ).

cnf(c_1766,plain,
    ( relation_dom(identity_relation(sK14)) != sK14
    | powerset(relation_dom(identity_relation(sK14))) = powerset(sK14) ),
    inference(instantiation,[status(thm)],[c_620]) ).

cnf(c_1767,plain,
    relation_dom(identity_relation(sK14)) = sK14,
    inference(instantiation,[status(thm)],[c_130]) ).

cnf(c_2063,plain,
    ( ~ element(sK15,powerset(X0))
    | ~ in(sK3(sK15),sK15)
    | ~ empty(X0) ),
    inference(instantiation,[status(thm)],[c_102]) ).

cnf(c_5303,plain,
    ( powerset(relation_dom(identity_relation(sK14))) != powerset(sK14)
    | sK15 != sK15
    | ~ element(sK15,powerset(sK14))
    | element(sK15,powerset(relation_dom(identity_relation(sK14)))) ),
    inference(instantiation,[status(thm)],[c_263]) ).

cnf(c_5572,plain,
    ( ~ element(X0,sK14)
    | in(X0,sK14)
    | empty(sK14) ),
    inference(instantiation,[status(thm)],[c_95]) ).

cnf(c_6113,plain,
    ( ~ in(sK0(identity_relation(sK14),sK15,sK15),sK15)
    | ~ element(sK15,powerset(sK14))
    | element(sK0(identity_relation(sK14),sK15,sK15),sK14) ),
    inference(instantiation,[status(thm)],[c_1677]) ).

cnf(c_6167,plain,
    ( ~ function(identity_relation(sK14))
    | ~ relation(identity_relation(sK14))
    | in(sK0(identity_relation(sK14),sK15,sK15),sK15)
    | in(sK1(identity_relation(sK14),sK15,sK15),sK15) ),
    inference(resolution,[status(thm)],[c_54,c_92]) ).

cnf(c_6216,plain,
    ( apply(X0,sK0(identity_relation(sK14),sK15,sK15)) != X1
    | sK0(X0,sK15,X2) != X1
    | sK0(X0,sK15,X2) = apply(X0,sK0(identity_relation(sK14),sK15,sK15)) ),
    inference(instantiation,[status(thm)],[c_163]) ).

cnf(c_6582,plain,
    ( ~ in(sK3(sK15),sK15)
    | ~ element(sK15,powerset(sK14))
    | ~ empty(sK14) ),
    inference(instantiation,[status(thm)],[c_2063]) ).

cnf(c_7192,plain,
    ( in(sK0(identity_relation(sK14),sK15,sK15),sK15)
    | in(sK1(identity_relation(sK14),sK15,sK15),sK15) ),
    inference(global_subsumption_just,[status(thm)],[c_6167,c_233,c_547,c_6167]) ).

cnf(c_7263,plain,
    ( ~ empty(sK15)
    | in(sK0(identity_relation(sK14),sK15,sK15),sK15) ),
    inference(resolution,[status(thm)],[c_7192,c_104]) ).

cnf(c_7265,plain,
    ~ empty(sK15),
    inference(global_subsumption_just,[status(thm)],[c_7263,c_1669,c_7263]) ).

cnf(c_11625,plain,
    ( ~ element(X0,relation_dom(identity_relation(sK14)))
    | in(X0,relation_dom(identity_relation(sK14)))
    | empty(relation_dom(identity_relation(sK14))) ),
    inference(instantiation,[status(thm)],[c_95]) ).

cnf(c_12153,plain,
    ( ~ element(sK15,powerset(relation_dom(identity_relation(sK14))))
    | ~ in(sK3(sK15),sK15)
    | ~ empty(relation_dom(identity_relation(sK14))) ),
    inference(instantiation,[status(thm)],[c_2063]) ).

cnf(c_12156,plain,
    ( ~ in(sK0(identity_relation(sK14),sK15,sK15),sK15)
    | ~ element(sK15,powerset(relation_dom(identity_relation(sK14))))
    | element(sK0(identity_relation(sK14),sK15,sK15),relation_dom(identity_relation(sK14))) ),
    inference(instantiation,[status(thm)],[c_1677]) ).

cnf(c_12471,plain,
    sK0(identity_relation(sK14),sK15,sK15) = sK0(identity_relation(sK14),sK15,sK15),
    inference(instantiation,[status(thm)],[c_161]) ).

cnf(c_13174,plain,
    ( apply(X0,sK0(identity_relation(sK14),sK15,sK15)) != sK0(X0,sK15,X1)
    | sK0(X0,sK15,X1) != sK0(X0,sK15,X1)
    | sK0(X0,sK15,X1) = apply(X0,sK0(identity_relation(sK14),sK15,sK15)) ),
    inference(instantiation,[status(thm)],[c_6216]) ).

cnf(c_14053,plain,
    ( ~ element(sK0(identity_relation(sK14),sK15,sK15),sK14)
    | in(sK0(identity_relation(sK14),sK15,sK15),sK14)
    | empty(sK14) ),
    inference(instantiation,[status(thm)],[c_5572]) ).

cnf(c_20190,plain,
    ( ~ in(sK0(identity_relation(sK14),sK15,sK15),sK14)
    | ~ function(identity_relation(sK14))
    | ~ relation(identity_relation(sK14))
    | apply(identity_relation(sK14),sK0(identity_relation(sK14),sK15,sK15)) = sK0(identity_relation(sK14),sK15,sK15) ),
    inference(instantiation,[status(thm)],[c_98]) ).

cnf(c_20719,plain,
    ( ~ element(sK0(identity_relation(sK14),sK15,sK15),relation_dom(identity_relation(sK14)))
    | in(sK0(identity_relation(sK14),sK15,sK15),relation_dom(identity_relation(sK14)))
    | empty(relation_dom(identity_relation(sK14))) ),
    inference(instantiation,[status(thm)],[c_11625]) ).

cnf(c_26386,plain,
    ( apply(identity_relation(sK14),sK0(identity_relation(sK14),sK15,sK15)) != sK0(identity_relation(sK14),sK15,sK15)
    | sK0(identity_relation(sK14),sK15,sK15) != sK0(identity_relation(sK14),sK15,sK15)
    | sK0(identity_relation(sK14),sK15,sK15) = apply(identity_relation(sK14),sK0(identity_relation(sK14),sK15,sK15)) ),
    inference(instantiation,[status(thm)],[c_13174]) ).

cnf(c_29101,plain,
    ( sK0(identity_relation(sK14),sK15,X0) != apply(identity_relation(sK14),sK0(identity_relation(sK14),sK15,sK15))
    | ~ in(sK0(identity_relation(sK14),sK15,sK15),relation_dom(identity_relation(sK14)))
    | ~ in(sK0(identity_relation(sK14),sK15,X0),X0)
    | ~ in(sK0(identity_relation(sK14),sK15,sK15),sK15)
    | ~ function(identity_relation(sK14))
    | ~ relation(identity_relation(sK14))
    | relation_image(identity_relation(sK14),sK15) = X0 ),
    inference(instantiation,[status(thm)],[c_1673]) ).

cnf(c_37696,plain,
    ( sK0(identity_relation(sK14),sK15,sK15) != apply(identity_relation(sK14),sK0(identity_relation(sK14),sK15,sK15))
    | ~ in(sK0(identity_relation(sK14),sK15,sK15),relation_dom(identity_relation(sK14)))
    | ~ in(sK0(identity_relation(sK14),sK15,sK15),sK15)
    | ~ function(identity_relation(sK14))
    | ~ relation(identity_relation(sK14))
    | relation_image(identity_relation(sK14),sK15) = sK15 ),
    inference(instantiation,[status(thm)],[c_29101]) ).

cnf(c_38743,plain,
    ( ~ in(sK1(identity_relation(sK14),sK15,sK15),sK15)
    | ~ element(sK15,powerset(X0))
    | element(sK1(identity_relation(sK14),sK15,sK15),X0) ),
    inference(instantiation,[status(thm)],[c_101]) ).

cnf(c_38745,plain,
    ( X0 != sK1(identity_relation(sK14),sK15,sK15)
    | X1 != sK15
    | ~ in(sK1(identity_relation(sK14),sK15,sK15),sK15)
    | in(X0,X1) ),
    inference(instantiation,[status(thm)],[c_164]) ).

cnf(c_39031,plain,
    ( ~ in(sK1(identity_relation(sK14),sK15,sK15),sK15)
    | ~ element(sK15,powerset(sK14))
    | element(sK1(identity_relation(sK14),sK15,sK15),sK14) ),
    inference(instantiation,[status(thm)],[c_38743]) ).

cnf(c_39093,plain,
    ( X0 != sK1(identity_relation(sK14),sK15,sK15)
    | sK15 != sK15
    | ~ in(sK1(identity_relation(sK14),sK15,sK15),sK15)
    | in(X0,sK15) ),
    inference(instantiation,[status(thm)],[c_38745]) ).

cnf(c_39158,plain,
    ( apply(X0,sK1(identity_relation(sK14),sK15,sK15)) != X1
    | sK0(X0,sK15,X2) != X1
    | sK0(X0,sK15,X2) = apply(X0,sK1(identity_relation(sK14),sK15,sK15)) ),
    inference(instantiation,[status(thm)],[c_163]) ).

cnf(c_39549,plain,
    ( ~ element(X0,sK14)
    | in(X0,sK14)
    | empty(sK14) ),
    inference(instantiation,[status(thm)],[c_95]) ).

cnf(c_40091,plain,
    ( apply(X0,sK1(identity_relation(sK14),sK15,sK15)) != sK0(X0,sK15,X1)
    | sK0(X0,sK15,X1) != sK0(X0,sK15,X1)
    | sK0(X0,sK15,X1) = apply(X0,sK1(identity_relation(sK14),sK15,sK15)) ),
    inference(instantiation,[status(thm)],[c_39158]) ).

cnf(c_41109,plain,
    ( ~ element(sK1(identity_relation(sK14),sK15,sK15),sK14)
    | in(sK1(identity_relation(sK14),sK15,sK15),sK14)
    | empty(sK14) ),
    inference(instantiation,[status(thm)],[c_39549]) ).

cnf(c_42959,plain,
    ( apply(identity_relation(sK14),sK1(identity_relation(sK14),sK15,sK15)) != sK0(identity_relation(sK14),sK15,sK15)
    | sK0(identity_relation(sK14),sK15,sK15) != sK0(identity_relation(sK14),sK15,sK15)
    | sK0(identity_relation(sK14),sK15,sK15) = apply(identity_relation(sK14),sK1(identity_relation(sK14),sK15,sK15)) ),
    inference(instantiation,[status(thm)],[c_40091]) ).

cnf(c_45409,plain,
    ( ~ in(sK1(identity_relation(sK14),sK15,sK15),sK14)
    | ~ function(identity_relation(sK14))
    | ~ relation(identity_relation(sK14))
    | apply(identity_relation(sK14),sK1(identity_relation(sK14),sK15,sK15)) = sK1(identity_relation(sK14),sK15,sK15) ),
    inference(instantiation,[status(thm)],[c_98]) ).

cnf(c_45611,plain,
    ( X0 != X1
    | X2 != sK15
    | ~ in(X1,sK15)
    | in(X0,X2) ),
    inference(instantiation,[status(thm)],[c_164]) ).

cnf(c_50090,plain,
    ( apply(identity_relation(sK14),sK1(identity_relation(sK14),sK15,sK15)) != sK1(identity_relation(sK14),sK15,sK15)
    | sK15 != sK15
    | ~ in(sK1(identity_relation(sK14),sK15,sK15),sK15)
    | in(apply(identity_relation(sK14),sK1(identity_relation(sK14),sK15,sK15)),sK15) ),
    inference(instantiation,[status(thm)],[c_39093]) ).

cnf(c_51188,plain,
    ( X0 != X1
    | sK15 != sK15
    | ~ in(X1,sK15)
    | in(X0,sK15) ),
    inference(instantiation,[status(thm)],[c_45611]) ).

cnf(c_55060,plain,
    ( X0 != apply(identity_relation(sK14),sK1(identity_relation(sK14),sK15,sK15))
    | sK15 != sK15
    | ~ in(apply(identity_relation(sK14),sK1(identity_relation(sK14),sK15,sK15)),sK15)
    | in(X0,sK15) ),
    inference(instantiation,[status(thm)],[c_51188]) ).

cnf(c_63512,plain,
    ( sK0(identity_relation(sK14),sK15,sK15) != apply(identity_relation(sK14),sK1(identity_relation(sK14),sK15,sK15))
    | sK15 != sK15
    | ~ in(apply(identity_relation(sK14),sK1(identity_relation(sK14),sK15,sK15)),sK15)
    | in(sK0(identity_relation(sK14),sK15,sK15),sK15) ),
    inference(instantiation,[status(thm)],[c_55060]) ).

cnf(c_63513,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_63512,c_50090,c_45409,c_42959,c_41109,c_39031,c_37696,c_26386,c_20719,c_20190,c_14053,c_12471,c_12153,c_12156,c_7265,c_7192,c_6582,c_6113,c_5303,c_1767,c_1766,c_1121,c_1120,c_547,c_264,c_233,c_204,c_92,c_93]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SEU081+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.14  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n002.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % 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 : Thu May  2 17:53:42 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.19/0.48  Running first-order theorem proving
% 0.19/0.48  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
% 61.81/9.27  % SZS status Started for theBenchmark.p
% 61.81/9.27  % SZS status Theorem for theBenchmark.p
% 61.81/9.27  
% 61.81/9.27  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 61.81/9.27  
% 61.81/9.27  ------  iProver source info
% 61.81/9.27  
% 61.81/9.27  git: date: 2024-05-02 19:28:25 +0000
% 61.81/9.27  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 61.81/9.27  git: non_committed_changes: false
% 61.81/9.27  
% 61.81/9.27  ------ Parsing...
% 61.81/9.27  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 61.81/9.27  
% 61.81/9.27  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 1 0s  sf_e 
% 61.81/9.27  
% 61.81/9.27  ------ Preprocessing...
% 61.81/9.27  
% 61.81/9.27  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 61.81/9.27  ------ Proving...
% 61.81/9.27  ------ Problem Properties 
% 61.81/9.27  
% 61.81/9.27  
% 61.81/9.27  clauses                                 53
% 61.81/9.27  conjectures                             2
% 61.81/9.27  EPR                                     25
% 61.81/9.27  Horn                                    47
% 61.81/9.27  unary                                   26
% 61.81/9.27  binary                                  11
% 61.81/9.27  lits                                    114
% 61.81/9.27  lits eq                                 15
% 61.81/9.27  fd_pure                                 0
% 61.81/9.27  fd_pseudo                               0
% 61.81/9.27  fd_cond                                 1
% 61.81/9.27  fd_pseudo_cond                          5
% 61.81/9.27  AC symbols                              0
% 61.81/9.27  
% 61.81/9.27  ------ Input Options Time Limit: Unbounded
% 61.81/9.27  
% 61.81/9.27  
% 61.81/9.27  ------ 
% 61.81/9.27  Current options:
% 61.81/9.27  ------ 
% 61.81/9.27  
% 61.81/9.27  
% 61.81/9.27  
% 61.81/9.27  
% 61.81/9.27  ------ Proving...
% 61.81/9.27  
% 61.81/9.27  
% 61.81/9.27  % SZS status Theorem for theBenchmark.p
% 61.81/9.27  
% 61.81/9.27  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 61.81/9.27  
% 61.81/9.27  
%------------------------------------------------------------------------------