TSTP Solution File: SEU228+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SEU228+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n022.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 17:04:57 EDT 2023

% Result   : Theorem 45.33s 6.74s
% Output   : CNFRefutation 45.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   28
% Syntax   : Number of formulae    :  154 (  19 unt;   0 def)
%            Number of atoms       :  707 ( 170 equ)
%            Maximal formula atoms :   20 (   4 avg)
%            Number of connectives :  916 ( 363   ~; 378   |; 132   &)
%                                         (  22 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   17 (  17 usr;   3 con; 0-3 aty)
%            Number of variables   :  339 (   3 sgn; 216   !;  41   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f5,axiom,
    ! [X0,X1] :
      ( X0 = X1
    <=> ( subset(X1,X0)
        & subset(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).

fof(f6,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] :
      ( ( function(X0)
        & relation(X0) )
     => ! [X1,X2] :
          ( relation_inverse_image(X0,X1) = X2
        <=> ! [X3] :
              ( in(X3,X2)
            <=> ( in(apply(X0,X3),X1)
                & in(X3,relation_dom(X0)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).

fof(f8,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

fof(f9,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(f22,axiom,
    ( relation(empty_set)
    & empty(empty_set) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).

fof(f37,axiom,
    ! [X0,X1] : subset(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

fof(f38,axiom,
    ! [X0,X1] :
      ( ( function(X1)
        & relation(X1) )
     => subset(relation_image(X1,relation_inverse_image(X1,X0)),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_funct_1) ).

fof(f39,conjecture,
    ! [X0,X1] :
      ( ( function(X1)
        & relation(X1) )
     => ( subset(X0,relation_rng(X1))
       => relation_image(X1,relation_inverse_image(X1,X0)) = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t147_funct_1) ).

fof(f40,negated_conjecture,
    ~ ! [X0,X1] :
        ( ( function(X1)
          & relation(X1) )
       => ( subset(X0,relation_rng(X1))
         => relation_image(X1,relation_inverse_image(X1,X0)) = X0 ) ),
    inference(negated_conjecture,[],[f39]) ).

fof(f41,axiom,
    ! [X0,X1] :
      ( in(X0,X1)
     => element(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).

fof(f42,axiom,
    ! [X0,X1] :
      ( element(X0,X1)
     => ( in(X0,X1)
        | empty(X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).

fof(f43,axiom,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).

fof(f45,axiom,
    ! [X0,X1,X2] :
      ~ ( empty(X2)
        & element(X1,powerset(X2))
        & in(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).

fof(f46,axiom,
    ! [X0] :
      ( empty(X0)
     => empty_set = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

fof(f49,plain,
    ! [X0] : subset(X0,X0),
    inference(rectify,[],[f37]) ).

fof(f59,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,[],[f6]) ).

fof(f60,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,[],[f59]) ).

fof(f61,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( relation_inverse_image(X0,X1) = X2
        <=> ! [X3] :
              ( in(X3,X2)
            <=> ( in(apply(X0,X3),X1)
                & in(X3,relation_dom(X0)) ) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f62,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( relation_inverse_image(X0,X1) = X2
        <=> ! [X3] :
              ( in(X3,X2)
            <=> ( in(apply(X0,X3),X1)
                & in(X3,relation_dom(X0)) ) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f61]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f64,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,[],[f9]) ).

fof(f65,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,[],[f64]) ).

fof(f73,plain,
    ! [X0,X1] :
      ( subset(relation_image(X1,relation_inverse_image(X1,X0)),X0)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( subset(relation_image(X1,relation_inverse_image(X1,X0)),X0)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(flattening,[],[f73]) ).

fof(f75,plain,
    ? [X0,X1] :
      ( relation_image(X1,relation_inverse_image(X1,X0)) != X0
      & subset(X0,relation_rng(X1))
      & function(X1)
      & relation(X1) ),
    inference(ennf_transformation,[],[f40]) ).

fof(f76,plain,
    ? [X0,X1] :
      ( relation_image(X1,relation_inverse_image(X1,X0)) != X0
      & subset(X0,relation_rng(X1))
      & function(X1)
      & relation(X1) ),
    inference(flattening,[],[f75]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( element(X0,X1)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f41]) ).

fof(f78,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(ennf_transformation,[],[f42]) ).

fof(f79,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(flattening,[],[f78]) ).

fof(f82,plain,
    ! [X0,X1,X2] :
      ( ~ empty(X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f45]) ).

fof(f83,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f46]) ).

fof(f86,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f5]) ).

fof(f87,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(flattening,[],[f86]) ).

fof(f88,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,[],[f60]) ).

fof(f89,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,[],[f88]) ).

fof(f90,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(f91,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(f92,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(f93,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])],[f89,f92,f91,f90]) ).

fof(f94,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( relation_inverse_image(X0,X1) = X2
            | ? [X3] :
                ( ( ~ in(apply(X0,X3),X1)
                  | ~ in(X3,relation_dom(X0))
                  | ~ in(X3,X2) )
                & ( ( in(apply(X0,X3),X1)
                    & in(X3,relation_dom(X0)) )
                  | in(X3,X2) ) ) )
          & ( ! [X3] :
                ( ( in(X3,X2)
                  | ~ in(apply(X0,X3),X1)
                  | ~ in(X3,relation_dom(X0)) )
                & ( ( in(apply(X0,X3),X1)
                    & in(X3,relation_dom(X0)) )
                  | ~ in(X3,X2) ) )
            | relation_inverse_image(X0,X1) != X2 ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f62]) ).

fof(f95,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( relation_inverse_image(X0,X1) = X2
            | ? [X3] :
                ( ( ~ in(apply(X0,X3),X1)
                  | ~ in(X3,relation_dom(X0))
                  | ~ in(X3,X2) )
                & ( ( in(apply(X0,X3),X1)
                    & in(X3,relation_dom(X0)) )
                  | in(X3,X2) ) ) )
          & ( ! [X3] :
                ( ( in(X3,X2)
                  | ~ in(apply(X0,X3),X1)
                  | ~ in(X3,relation_dom(X0)) )
                & ( ( in(apply(X0,X3),X1)
                    & in(X3,relation_dom(X0)) )
                  | ~ in(X3,X2) ) )
            | relation_inverse_image(X0,X1) != X2 ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f94]) ).

fof(f96,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( relation_inverse_image(X0,X1) = X2
            | ? [X3] :
                ( ( ~ in(apply(X0,X3),X1)
                  | ~ in(X3,relation_dom(X0))
                  | ~ in(X3,X2) )
                & ( ( in(apply(X0,X3),X1)
                    & in(X3,relation_dom(X0)) )
                  | in(X3,X2) ) ) )
          & ( ! [X4] :
                ( ( in(X4,X2)
                  | ~ in(apply(X0,X4),X1)
                  | ~ in(X4,relation_dom(X0)) )
                & ( ( in(apply(X0,X4),X1)
                    & in(X4,relation_dom(X0)) )
                  | ~ in(X4,X2) ) )
            | relation_inverse_image(X0,X1) != X2 ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(rectify,[],[f95]) ).

fof(f97,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ in(apply(X0,X3),X1)
            | ~ in(X3,relation_dom(X0))
            | ~ in(X3,X2) )
          & ( ( in(apply(X0,X3),X1)
              & in(X3,relation_dom(X0)) )
            | in(X3,X2) ) )
     => ( ( ~ in(apply(X0,sK3(X0,X1,X2)),X1)
          | ~ in(sK3(X0,X1,X2),relation_dom(X0))
          | ~ in(sK3(X0,X1,X2),X2) )
        & ( ( in(apply(X0,sK3(X0,X1,X2)),X1)
            & in(sK3(X0,X1,X2),relation_dom(X0)) )
          | in(sK3(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f98,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( relation_inverse_image(X0,X1) = X2
            | ( ( ~ in(apply(X0,sK3(X0,X1,X2)),X1)
                | ~ in(sK3(X0,X1,X2),relation_dom(X0))
                | ~ in(sK3(X0,X1,X2),X2) )
              & ( ( in(apply(X0,sK3(X0,X1,X2)),X1)
                  & in(sK3(X0,X1,X2),relation_dom(X0)) )
                | in(sK3(X0,X1,X2),X2) ) ) )
          & ( ! [X4] :
                ( ( in(X4,X2)
                  | ~ in(apply(X0,X4),X1)
                  | ~ in(X4,relation_dom(X0)) )
                & ( ( in(apply(X0,X4),X1)
                    & in(X4,relation_dom(X0)) )
                  | ~ in(X4,X2) ) )
            | relation_inverse_image(X0,X1) != X2 ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f96,f97]) ).

fof(f99,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,[],[f63]) ).

fof(f100,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,[],[f99]) ).

fof(f101,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK4(X0,X1),X1)
        & in(sK4(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f102,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK4(X0,X1),X1)
          & in(sK4(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f100,f101]) ).

fof(f103,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,[],[f65]) ).

fof(f104,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,[],[f103]) ).

fof(f105,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) != sK5(X0,X1)
              | ~ in(X3,relation_dom(X0)) )
          | ~ in(sK5(X0,X1),X1) )
        & ( ? [X4] :
              ( apply(X0,X4) = sK5(X0,X1)
              & in(X4,relation_dom(X0)) )
          | in(sK5(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f106,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( apply(X0,X4) = sK5(X0,X1)
          & in(X4,relation_dom(X0)) )
     => ( sK5(X0,X1) = apply(X0,sK6(X0,X1))
        & in(sK6(X0,X1),relation_dom(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f107,plain,
    ! [X0,X5] :
      ( ? [X7] :
          ( apply(X0,X7) = X5
          & in(X7,relation_dom(X0)) )
     => ( apply(X0,sK7(X0,X5)) = X5
        & in(sK7(X0,X5),relation_dom(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f108,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_rng(X0) = X1
            | ( ( ! [X3] :
                    ( apply(X0,X3) != sK5(X0,X1)
                    | ~ in(X3,relation_dom(X0)) )
                | ~ in(sK5(X0,X1),X1) )
              & ( ( sK5(X0,X1) = apply(X0,sK6(X0,X1))
                  & in(sK6(X0,X1),relation_dom(X0)) )
                | in(sK5(X0,X1),X1) ) ) )
          & ( ! [X5] :
                ( ( in(X5,X1)
                  | ! [X6] :
                      ( apply(X0,X6) != X5
                      | ~ in(X6,relation_dom(X0)) ) )
                & ( ( apply(X0,sK7(X0,X5)) = X5
                    & in(sK7(X0,X5),relation_dom(X0)) )
                  | ~ in(X5,X1) ) )
            | relation_rng(X0) != X1 ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f104,f107,f106,f105]) ).

fof(f131,plain,
    ( ? [X0,X1] :
        ( relation_image(X1,relation_inverse_image(X1,X0)) != X0
        & subset(X0,relation_rng(X1))
        & function(X1)
        & relation(X1) )
   => ( sK19 != relation_image(sK20,relation_inverse_image(sK20,sK19))
      & subset(sK19,relation_rng(sK20))
      & function(sK20)
      & relation(sK20) ) ),
    introduced(choice_axiom,[]) ).

fof(f132,plain,
    ( sK19 != relation_image(sK20,relation_inverse_image(sK20,sK19))
    & subset(sK19,relation_rng(sK20))
    & function(sK20)
    & relation(sK20) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK19,sK20])],[f76,f131]) ).

fof(f133,plain,
    ! [X0,X1] :
      ( ( element(X0,powerset(X1))
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ~ element(X0,powerset(X1)) ) ),
    inference(nnf_transformation,[],[f43]) ).

fof(f141,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f87]) ).

fof(f147,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,[],[f93]) ).

fof(f148,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,[],[f93]) ).

fof(f149,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,[],[f93]) ).

fof(f151,plain,
    ! [X2,X0,X1,X4] :
      ( in(apply(X0,X4),X1)
      | ~ in(X4,X2)
      | relation_inverse_image(X0,X1) != X2
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f98]) ).

fof(f152,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X2)
      | ~ in(apply(X0,X4),X1)
      | ~ in(X4,relation_dom(X0))
      | relation_inverse_image(X0,X1) != X2
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f98]) ).

fof(f156,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | ~ in(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f157,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sK4(X0,X1),X0) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f159,plain,
    ! [X0,X1,X5] :
      ( in(sK7(X0,X5),relation_dom(X0))
      | ~ in(X5,X1)
      | relation_rng(X0) != X1
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f108]) ).

fof(f160,plain,
    ! [X0,X1,X5] :
      ( apply(X0,sK7(X0,X5)) = X5
      | ~ in(X5,X1)
      | relation_rng(X0) != X1
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f108]) ).

fof(f170,plain,
    empty(empty_set),
    inference(cnf_transformation,[],[f22]) ).

fof(f196,plain,
    ! [X0] : subset(X0,X0),
    inference(cnf_transformation,[],[f49]) ).

fof(f197,plain,
    ! [X0,X1] :
      ( subset(relation_image(X1,relation_inverse_image(X1,X0)),X0)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f198,plain,
    relation(sK20),
    inference(cnf_transformation,[],[f132]) ).

fof(f199,plain,
    function(sK20),
    inference(cnf_transformation,[],[f132]) ).

fof(f200,plain,
    subset(sK19,relation_rng(sK20)),
    inference(cnf_transformation,[],[f132]) ).

fof(f201,plain,
    sK19 != relation_image(sK20,relation_inverse_image(sK20,sK19)),
    inference(cnf_transformation,[],[f132]) ).

fof(f202,plain,
    ! [X0,X1] :
      ( element(X0,X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f203,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f205,plain,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f133]) ).

fof(f207,plain,
    ! [X2,X0,X1] :
      ( ~ empty(X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f82]) ).

fof(f208,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f218,plain,
    ! [X0,X1,X4] :
      ( in(X4,relation_inverse_image(X0,X1))
      | ~ in(apply(X0,X4),X1)
      | ~ in(X4,relation_dom(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f152]) ).

fof(f219,plain,
    ! [X0,X1,X4] :
      ( in(apply(X0,X4),X1)
      | ~ in(X4,relation_inverse_image(X0,X1))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f151]) ).

fof(f223,plain,
    ! [X0,X5] :
      ( apply(X0,sK7(X0,X5)) = X5
      | ~ in(X5,relation_rng(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f160]) ).

fof(f224,plain,
    ! [X0,X5] :
      ( in(sK7(X0,X5),relation_dom(X0))
      | ~ in(X5,relation_rng(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f159]) ).

cnf(c_52,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X1,X0)
    | X0 = X1 ),
    inference(cnf_transformation,[],[f141]) ).

cnf(c_55,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,[],[f149]) ).

cnf(c_56,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,[],[f148]) ).

cnf(c_57,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,[],[f147]) ).

cnf(c_66,plain,
    ( ~ in(apply(X0,X1),X2)
    | ~ in(X1,relation_dom(X0))
    | ~ function(X0)
    | ~ relation(X0)
    | in(X1,relation_inverse_image(X0,X2)) ),
    inference(cnf_transformation,[],[f218]) ).

cnf(c_67,plain,
    ( ~ in(X0,relation_inverse_image(X1,X2))
    | ~ function(X1)
    | ~ relation(X1)
    | in(apply(X1,X0),X2) ),
    inference(cnf_transformation,[],[f219]) ).

cnf(c_70,plain,
    ( in(sK4(X0,X1),X0)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f157]) ).

cnf(c_71,plain,
    ( ~ in(X0,X1)
    | ~ subset(X1,X2)
    | in(X0,X2) ),
    inference(cnf_transformation,[],[f156]) ).

cnf(c_76,plain,
    ( ~ in(X0,relation_rng(X1))
    | ~ function(X1)
    | ~ relation(X1)
    | apply(X1,sK7(X1,X0)) = X0 ),
    inference(cnf_transformation,[],[f223]) ).

cnf(c_77,plain,
    ( ~ in(X0,relation_rng(X1))
    | ~ function(X1)
    | ~ relation(X1)
    | in(sK7(X1,X0),relation_dom(X1)) ),
    inference(cnf_transformation,[],[f224]) ).

cnf(c_84,plain,
    empty(empty_set),
    inference(cnf_transformation,[],[f170]) ).

cnf(c_109,plain,
    subset(X0,X0),
    inference(cnf_transformation,[],[f196]) ).

cnf(c_110,plain,
    ( ~ function(X0)
    | ~ relation(X0)
    | subset(relation_image(X0,relation_inverse_image(X0,X1)),X1) ),
    inference(cnf_transformation,[],[f197]) ).

cnf(c_111,negated_conjecture,
    relation_image(sK20,relation_inverse_image(sK20,sK19)) != sK19,
    inference(cnf_transformation,[],[f201]) ).

cnf(c_112,negated_conjecture,
    subset(sK19,relation_rng(sK20)),
    inference(cnf_transformation,[],[f200]) ).

cnf(c_113,negated_conjecture,
    function(sK20),
    inference(cnf_transformation,[],[f199]) ).

cnf(c_114,negated_conjecture,
    relation(sK20),
    inference(cnf_transformation,[],[f198]) ).

cnf(c_115,plain,
    ( ~ in(X0,X1)
    | element(X0,X1) ),
    inference(cnf_transformation,[],[f202]) ).

cnf(c_116,plain,
    ( ~ element(X0,X1)
    | in(X0,X1)
    | empty(X1) ),
    inference(cnf_transformation,[],[f203]) ).

cnf(c_117,plain,
    ( ~ subset(X0,X1)
    | element(X0,powerset(X1)) ),
    inference(cnf_transformation,[],[f205]) ).

cnf(c_120,plain,
    ( ~ element(X0,powerset(X1))
    | ~ in(X2,X0)
    | ~ empty(X1) ),
    inference(cnf_transformation,[],[f207]) ).

cnf(c_121,plain,
    ( ~ empty(X0)
    | X0 = empty_set ),
    inference(cnf_transformation,[],[f208]) ).

cnf(c_124,plain,
    subset(empty_set,empty_set),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_135,plain,
    ( ~ empty(empty_set)
    | empty_set = empty_set ),
    inference(instantiation,[status(thm)],[c_121]) ).

cnf(c_161,plain,
    ( ~ subset(X0,X1)
    | element(X0,powerset(X1)) ),
    inference(prop_impl_just,[status(thm)],[c_117]) ).

cnf(c_324,plain,
    ( ~ in(X0,X1)
    | ~ subset(X1,X2)
    | ~ empty(X2) ),
    inference(bin_hyper_res,[status(thm)],[c_120,c_161]) ).

cnf(c_13753,plain,
    X0 = X0,
    theory(equality) ).

cnf(c_13755,plain,
    ( X0 != X1
    | X2 != X1
    | X2 = X0 ),
    theory(equality) ).

cnf(c_13756,plain,
    ( X0 != X1
    | X2 != X3
    | ~ in(X1,X3)
    | in(X0,X2) ),
    theory(equality) ).

cnf(c_13760,plain,
    ( X0 != X1
    | X2 != X3
    | ~ subset(X1,X3)
    | subset(X0,X2) ),
    theory(equality) ).

cnf(c_13765,plain,
    ( X0 != X1
    | X2 != X3
    | ~ element(X1,X3)
    | element(X0,X2) ),
    theory(equality) ).

cnf(c_15662,plain,
    ( ~ subset(relation_image(sK20,relation_inverse_image(sK20,sK19)),sK19)
    | ~ subset(sK19,relation_image(sK20,relation_inverse_image(sK20,sK19)))
    | relation_image(sK20,relation_inverse_image(sK20,sK19)) = sK19 ),
    inference(instantiation,[status(thm)],[c_52]) ).

cnf(c_15722,plain,
    ( ~ function(sK20)
    | ~ relation(sK20)
    | relation_image(sK20,relation_inverse_image(sK20,sK19)) = sK19
    | in(sK1(sK20,relation_inverse_image(sK20,sK19),sK19),relation_inverse_image(sK20,sK19))
    | in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),sK19) ),
    inference(instantiation,[status(thm)],[c_57]) ).

cnf(c_15779,plain,
    ( ~ function(sK20)
    | ~ relation(sK20)
    | apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19)) = sK0(sK20,relation_inverse_image(sK20,sK19),sK19)
    | relation_image(sK20,relation_inverse_image(sK20,sK19)) = sK19
    | in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),sK19) ),
    inference(instantiation,[status(thm)],[c_56]) ).

cnf(c_15780,plain,
    ( sK0(sK20,relation_inverse_image(sK20,sK19),sK19) != apply(sK20,X0)
    | ~ in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),sK19)
    | ~ in(X0,relation_inverse_image(sK20,sK19))
    | ~ in(X0,relation_dom(sK20))
    | ~ function(sK20)
    | ~ relation(sK20)
    | relation_image(sK20,relation_inverse_image(sK20,sK19)) = sK19 ),
    inference(instantiation,[status(thm)],[c_55]) ).

cnf(c_16027,plain,
    ( ~ element(X0,sK19)
    | in(X0,sK19)
    | empty(sK19) ),
    inference(instantiation,[status(thm)],[c_116]) ).

cnf(c_16093,plain,
    ( ~ function(sK20)
    | ~ relation(sK20)
    | subset(relation_image(sK20,relation_inverse_image(sK20,sK19)),sK19) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_16129,plain,
    ( ~ in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),sK19)
    | ~ subset(sK19,X0)
    | in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),X0) ),
    inference(instantiation,[status(thm)],[c_71]) ).

cnf(c_16136,plain,
    ( X0 != sK0(sK20,relation_inverse_image(sK20,sK19),sK19)
    | X1 != sK19
    | ~ in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),sK19)
    | in(X0,X1) ),
    inference(instantiation,[status(thm)],[c_13756]) ).

cnf(c_16237,plain,
    ( ~ subset(X0,sK19)
    | ~ subset(sK19,X0)
    | sK19 = X0 ),
    inference(instantiation,[status(thm)],[c_52]) ).

cnf(c_16242,plain,
    ( ~ empty(sK19)
    | sK19 = empty_set ),
    inference(instantiation,[status(thm)],[c_121]) ).

cnf(c_17797,plain,
    ( in(sK4(sK19,relation_image(sK20,relation_inverse_image(sK20,sK19))),sK19)
    | subset(sK19,relation_image(sK20,relation_inverse_image(sK20,sK19))) ),
    inference(instantiation,[status(thm)],[c_70]) ).

cnf(c_17904,plain,
    ( ~ in(sK1(sK20,relation_inverse_image(sK20,sK19),sK19),relation_inverse_image(sK20,sK19))
    | ~ function(sK20)
    | ~ relation(sK20)
    | in(apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19)),sK19) ),
    inference(instantiation,[status(thm)],[c_67]) ).

cnf(c_20986,plain,
    ( ~ subset(sK19,sK19)
    | sK19 = sK19 ),
    inference(instantiation,[status(thm)],[c_16237]) ).

cnf(c_20987,plain,
    subset(sK19,sK19),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_21448,plain,
    ( ~ element(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),sK19)
    | in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),sK19)
    | empty(sK19) ),
    inference(instantiation,[status(thm)],[c_16027]) ).

cnf(c_21573,plain,
    ( X0 != X1
    | sK19 != X2
    | ~ subset(X2,X1)
    | subset(sK19,X0) ),
    inference(instantiation,[status(thm)],[c_13760]) ).

cnf(c_21574,plain,
    ( empty_set != empty_set
    | sK19 != empty_set
    | ~ subset(empty_set,empty_set)
    | subset(sK19,empty_set) ),
    inference(instantiation,[status(thm)],[c_21573]) ).

cnf(c_21579,plain,
    ( ~ in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),sK19)
    | ~ subset(sK19,relation_rng(sK20))
    | in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),relation_rng(sK20)) ),
    inference(instantiation,[status(thm)],[c_16129]) ).

cnf(c_22528,plain,
    ( ~ in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),relation_rng(sK20))
    | ~ function(sK20)
    | ~ relation(sK20)
    | apply(sK20,sK7(sK20,sK0(sK20,relation_inverse_image(sK20,sK19),sK19))) = sK0(sK20,relation_inverse_image(sK20,sK19),sK19) ),
    inference(instantiation,[status(thm)],[c_76]) ).

cnf(c_22529,plain,
    ( ~ in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),relation_rng(sK20))
    | ~ function(sK20)
    | ~ relation(sK20)
    | in(sK7(sK20,sK0(sK20,relation_inverse_image(sK20,sK19),sK19)),relation_dom(sK20)) ),
    inference(instantiation,[status(thm)],[c_77]) ).

cnf(c_22862,plain,
    ( ~ in(sK4(sK19,relation_image(sK20,relation_inverse_image(sK20,sK19))),sK19)
    | ~ subset(sK19,X0)
    | ~ empty(X0) ),
    inference(instantiation,[status(thm)],[c_324]) ).

cnf(c_22863,plain,
    ( ~ in(sK4(sK19,relation_image(sK20,relation_inverse_image(sK20,sK19))),sK19)
    | ~ subset(sK19,empty_set)
    | ~ empty(empty_set) ),
    inference(instantiation,[status(thm)],[c_22862]) ).

cnf(c_24007,plain,
    ( X0 != sK0(sK20,relation_inverse_image(sK20,sK19),sK19)
    | sK19 != sK19
    | ~ in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),sK19)
    | in(X0,sK19) ),
    inference(instantiation,[status(thm)],[c_16136]) ).

cnf(c_26172,plain,
    sK0(sK20,relation_inverse_image(sK20,sK19),sK19) = sK0(sK20,relation_inverse_image(sK20,sK19),sK19),
    inference(instantiation,[status(thm)],[c_13753]) ).

cnf(c_37422,plain,
    ( ~ in(apply(sK20,sK7(sK20,sK0(sK20,relation_inverse_image(sK20,sK19),sK19))),X0)
    | ~ in(sK7(sK20,sK0(sK20,relation_inverse_image(sK20,sK19),sK19)),relation_dom(sK20))
    | ~ function(sK20)
    | ~ relation(sK20)
    | in(sK7(sK20,sK0(sK20,relation_inverse_image(sK20,sK19),sK19)),relation_inverse_image(sK20,X0)) ),
    inference(instantiation,[status(thm)],[c_66]) ).

cnf(c_37428,plain,
    ( sK0(sK20,relation_inverse_image(sK20,sK19),sK19) != apply(sK20,sK7(sK20,sK0(sK20,relation_inverse_image(sK20,sK19),sK19)))
    | ~ in(sK7(sK20,sK0(sK20,relation_inverse_image(sK20,sK19),sK19)),relation_inverse_image(sK20,sK19))
    | ~ in(sK7(sK20,sK0(sK20,relation_inverse_image(sK20,sK19),sK19)),relation_dom(sK20))
    | ~ in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),sK19)
    | ~ function(sK20)
    | ~ relation(sK20)
    | relation_image(sK20,relation_inverse_image(sK20,sK19)) = sK19 ),
    inference(instantiation,[status(thm)],[c_15780]) ).

cnf(c_64647,plain,
    ( ~ in(apply(sK20,sK7(sK20,sK0(sK20,relation_inverse_image(sK20,sK19),sK19))),sK19)
    | ~ in(sK7(sK20,sK0(sK20,relation_inverse_image(sK20,sK19),sK19)),relation_dom(sK20))
    | ~ function(sK20)
    | ~ relation(sK20)
    | in(sK7(sK20,sK0(sK20,relation_inverse_image(sK20,sK19),sK19)),relation_inverse_image(sK20,sK19)) ),
    inference(instantiation,[status(thm)],[c_37422]) ).

cnf(c_64649,plain,
    ( apply(sK20,sK7(sK20,sK0(sK20,relation_inverse_image(sK20,sK19),sK19))) != sK0(sK20,relation_inverse_image(sK20,sK19),sK19)
    | sK19 != sK19
    | ~ in(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),sK19)
    | in(apply(sK20,sK7(sK20,sK0(sK20,relation_inverse_image(sK20,sK19),sK19))),sK19) ),
    inference(instantiation,[status(thm)],[c_24007]) ).

cnf(c_90485,plain,
    ( apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19)) != X0
    | sK0(sK20,relation_inverse_image(sK20,sK19),X1) != X0
    | sK0(sK20,relation_inverse_image(sK20,sK19),X1) = apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19)) ),
    inference(instantiation,[status(thm)],[c_13755]) ).

cnf(c_103120,plain,
    ( apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19)) != sK0(sK20,relation_inverse_image(sK20,sK19),sK19)
    | sK0(sK20,relation_inverse_image(sK20,sK19),X0) != sK0(sK20,relation_inverse_image(sK20,sK19),sK19)
    | sK0(sK20,relation_inverse_image(sK20,sK19),X0) = apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19)) ),
    inference(instantiation,[status(thm)],[c_90485]) ).

cnf(c_112579,plain,
    ( apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19)) != sK0(sK20,relation_inverse_image(sK20,sK19),sK19)
    | sK0(sK20,relation_inverse_image(sK20,sK19),sK19) != sK0(sK20,relation_inverse_image(sK20,sK19),sK19)
    | sK0(sK20,relation_inverse_image(sK20,sK19),sK19) = apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19)) ),
    inference(instantiation,[status(thm)],[c_103120]) ).

cnf(c_121654,plain,
    ( ~ in(apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19)),sK19)
    | element(apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19)),sK19) ),
    inference(instantiation,[status(thm)],[c_115]) ).

cnf(c_122323,plain,
    ( X0 != apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19))
    | X1 != sK19
    | ~ element(apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19)),sK19)
    | element(X0,X1) ),
    inference(instantiation,[status(thm)],[c_13765]) ).

cnf(c_131217,plain,
    ( X0 != apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19))
    | sK19 != sK19
    | ~ element(apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19)),sK19)
    | element(X0,sK19) ),
    inference(instantiation,[status(thm)],[c_122323]) ).

cnf(c_138002,plain,
    ( sK0(sK20,relation_inverse_image(sK20,sK19),sK19) != X0
    | apply(sK20,X1) != X0
    | sK0(sK20,relation_inverse_image(sK20,sK19),sK19) = apply(sK20,X1) ),
    inference(instantiation,[status(thm)],[c_13755]) ).

cnf(c_143658,plain,
    ( sK0(sK20,relation_inverse_image(sK20,sK19),sK19) != sK0(sK20,relation_inverse_image(sK20,sK19),sK19)
    | apply(sK20,X0) != sK0(sK20,relation_inverse_image(sK20,sK19),sK19)
    | sK0(sK20,relation_inverse_image(sK20,sK19),sK19) = apply(sK20,X0) ),
    inference(instantiation,[status(thm)],[c_138002]) ).

cnf(c_166865,plain,
    ( apply(sK20,sK7(sK20,sK0(sK20,relation_inverse_image(sK20,sK19),sK19))) != sK0(sK20,relation_inverse_image(sK20,sK19),sK19)
    | sK0(sK20,relation_inverse_image(sK20,sK19),sK19) != sK0(sK20,relation_inverse_image(sK20,sK19),sK19)
    | sK0(sK20,relation_inverse_image(sK20,sK19),sK19) = apply(sK20,sK7(sK20,sK0(sK20,relation_inverse_image(sK20,sK19),sK19))) ),
    inference(instantiation,[status(thm)],[c_143658]) ).

cnf(c_187465,plain,
    ( sK0(sK20,relation_inverse_image(sK20,sK19),sK19) != apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19))
    | sK19 != sK19
    | ~ element(apply(sK20,sK1(sK20,relation_inverse_image(sK20,sK19),sK19)),sK19)
    | element(sK0(sK20,relation_inverse_image(sK20,sK19),sK19),sK19) ),
    inference(instantiation,[status(thm)],[c_131217]) ).

cnf(c_187469,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_187465,c_166865,c_121654,c_112579,c_64649,c_64647,c_37428,c_26172,c_22863,c_22528,c_22529,c_21579,c_21574,c_21448,c_20987,c_20986,c_17904,c_17797,c_16242,c_16093,c_15779,c_15722,c_15662,c_111,c_135,c_112,c_124,c_84,c_113,c_114]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU228+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.12/0.33  % Computer : n022.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Wed Aug 23 22:31:41 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.18/0.45  Running first-order theorem proving
% 0.18/0.45  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 45.33/6.74  % SZS status Started for theBenchmark.p
% 45.33/6.74  % SZS status Theorem for theBenchmark.p
% 45.33/6.74  
% 45.33/6.74  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 45.33/6.74  
% 45.33/6.74  ------  iProver source info
% 45.33/6.74  
% 45.33/6.74  git: date: 2023-05-31 18:12:56 +0000
% 45.33/6.74  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 45.33/6.74  git: non_committed_changes: false
% 45.33/6.74  git: last_make_outside_of_git: false
% 45.33/6.74  
% 45.33/6.74  ------ Parsing...
% 45.33/6.74  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 45.33/6.74  
% 45.33/6.74  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 45.33/6.74  
% 45.33/6.74  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 45.33/6.74  
% 45.33/6.74  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 45.33/6.74  ------ Proving...
% 45.33/6.74  ------ Problem Properties 
% 45.33/6.74  
% 45.33/6.74  
% 45.33/6.74  clauses                                 70
% 45.33/6.74  conjectures                             4
% 45.33/6.74  EPR                                     31
% 45.33/6.74  Horn                                    60
% 45.33/6.74  unary                                   25
% 45.33/6.74  binary                                  16
% 45.33/6.74  lits                                    180
% 45.33/6.74  lits eq                                 20
% 45.33/6.74  fd_pure                                 0
% 45.33/6.74  fd_pseudo                               0
% 45.33/6.74  fd_cond                                 1
% 45.33/6.74  fd_pseudo_cond                          12
% 45.33/6.74  AC symbols                              0
% 45.33/6.74  
% 45.33/6.74  ------ Schedule dynamic 5 is on 
% 45.33/6.74  
% 45.33/6.74  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 45.33/6.74  
% 45.33/6.74  
% 45.33/6.74  ------ 
% 45.33/6.74  Current options:
% 45.33/6.74  ------ 
% 45.33/6.74  
% 45.33/6.74  
% 45.33/6.74  
% 45.33/6.74  
% 45.33/6.74  ------ Proving...
% 45.33/6.74  
% 45.33/6.74  
% 45.33/6.74  % SZS status Theorem for theBenchmark.p
% 45.33/6.74  
% 45.33/6.74  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 45.33/6.74  
% 45.33/6.75  
%------------------------------------------------------------------------------