TSTP Solution File: SEU061+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SEU061+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 17:03:35 EDT 2023

% Result   : Theorem 109.60s 15.37s
% Output   : CNFRefutation 109.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   31
% Syntax   : Number of formulae    :  183 (  25 unt;   0 def)
%            Number of atoms       :  608 ( 151 equ)
%            Maximal formula atoms :   15 (   3 avg)
%            Number of connectives :  731 ( 306   ~; 323   |;  67   &)
%                                         (  14 <=>;  20  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   17 (  17 usr;   3 con; 0-3 aty)
%            Number of variables   :  353 (   8 sgn; 217   !;  40   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [X0] :
      ( empty(X0)
     => relation(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).

fof(f6,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X1,X2] :
          ( relation_inverse_image(X0,X1) = X2
        <=> ! [X3] :
              ( in(X3,X2)
            <=> ? [X4] :
                  ( in(X4,X1)
                  & in(ordered_pair(X3,X4),X0) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_1) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( singleton(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).

fof(f8,axiom,
    ! [X0] :
      ( empty_set = X0
    <=> ! [X1] : ~ in(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).

fof(f9,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X1] :
          ( relation_rng(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).

fof(f10,axiom,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).

fof(f16,axiom,
    ! [X0] : ~ empty(singleton(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).

fof(f18,axiom,
    ( relation(empty_set)
    & empty(empty_set) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).

fof(f19,axiom,
    ! [X0] :
      ( ( relation(X0)
        & ~ empty(X0) )
     => ~ empty(relation_rng(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).

fof(f20,axiom,
    ! [X0] :
      ( empty(X0)
     => ( relation(relation_rng(X0))
        & empty(relation_rng(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).

fof(f31,axiom,
    ! [X0,X1] : subset(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

fof(f32,conjecture,
    ! [X0,X1] :
      ( relation(X1)
     => ( in(X0,relation_rng(X1))
      <=> empty_set != relation_inverse_image(X1,singleton(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t142_funct_1) ).

fof(f33,negated_conjecture,
    ~ ! [X0,X1] :
        ( relation(X1)
       => ( in(X0,relation_rng(X1))
        <=> empty_set != relation_inverse_image(X1,singleton(X0)) ) ),
    inference(negated_conjecture,[],[f32]) ).

fof(f35,axiom,
    ! [X0,X1] :
      ( element(X0,X1)
     => ( in(X0,X1)
        | empty(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).

fof(f36,axiom,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).

fof(f37,axiom,
    ! [X0,X1,X2] :
      ( ( element(X1,powerset(X2))
        & in(X0,X1) )
     => element(X0,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).

fof(f39,axiom,
    ! [X0] :
      ( empty(X0)
     => empty_set = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

fof(f40,axiom,
    ! [X0,X1] :
      ~ ( empty(X1)
        & in(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).

fof(f42,plain,
    ! [X0] : subset(X0,X0),
    inference(rectify,[],[f31]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
     => element(X0,powerset(X1)) ),
    inference(unused_predicate_definition_removal,[],[f36]) ).

fof(f50,plain,
    ! [X0] :
      ( relation(X0)
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f53,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( relation_inverse_image(X0,X1) = X2
        <=> ! [X3] :
              ( in(X3,X2)
            <=> ? [X4] :
                  ( in(X4,X1)
                  & in(ordered_pair(X3,X4),X0) ) ) )
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f54,plain,
    ! [X0] :
      ( ! [X1] :
          ( relation_rng(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f55,plain,
    ! [X0] :
      ( ~ empty(relation_rng(X0))
      | ~ relation(X0)
      | empty(X0) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f56,plain,
    ! [X0] :
      ( ~ empty(relation_rng(X0))
      | ~ relation(X0)
      | empty(X0) ),
    inference(flattening,[],[f55]) ).

fof(f57,plain,
    ! [X0] :
      ( ( relation(relation_rng(X0))
        & empty(relation_rng(X0)) )
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f59,plain,
    ? [X0,X1] :
      ( ( in(X0,relation_rng(X1))
      <~> empty_set != relation_inverse_image(X1,singleton(X0)) )
      & relation(X1) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(ennf_transformation,[],[f35]) ).

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

fof(f63,plain,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f43]) ).

fof(f64,plain,
    ! [X0,X1,X2] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f65,plain,
    ! [X0,X1,X2] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(flattening,[],[f64]) ).

fof(f67,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f39]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f40]) ).

fof(f70,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( relation_inverse_image(X0,X1) = X2
            | ? [X3] :
                ( ( ! [X4] :
                      ( ~ in(X4,X1)
                      | ~ in(ordered_pair(X3,X4),X0) )
                  | ~ in(X3,X2) )
                & ( ? [X4] :
                      ( in(X4,X1)
                      & in(ordered_pair(X3,X4),X0) )
                  | in(X3,X2) ) ) )
          & ( ! [X3] :
                ( ( in(X3,X2)
                  | ! [X4] :
                      ( ~ in(X4,X1)
                      | ~ in(ordered_pair(X3,X4),X0) ) )
                & ( ? [X4] :
                      ( in(X4,X1)
                      & in(ordered_pair(X3,X4),X0) )
                  | ~ in(X3,X2) ) )
            | relation_inverse_image(X0,X1) != X2 ) )
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f53]) ).

fof(f71,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( relation_inverse_image(X0,X1) = X2
            | ? [X3] :
                ( ( ! [X4] :
                      ( ~ in(X4,X1)
                      | ~ in(ordered_pair(X3,X4),X0) )
                  | ~ in(X3,X2) )
                & ( ? [X5] :
                      ( in(X5,X1)
                      & in(ordered_pair(X3,X5),X0) )
                  | in(X3,X2) ) ) )
          & ( ! [X6] :
                ( ( in(X6,X2)
                  | ! [X7] :
                      ( ~ in(X7,X1)
                      | ~ in(ordered_pair(X6,X7),X0) ) )
                & ( ? [X8] :
                      ( in(X8,X1)
                      & in(ordered_pair(X6,X8),X0) )
                  | ~ in(X6,X2) ) )
            | relation_inverse_image(X0,X1) != X2 ) )
      | ~ relation(X0) ),
    inference(rectify,[],[f70]) ).

fof(f72,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ! [X4] :
                ( ~ in(X4,X1)
                | ~ in(ordered_pair(X3,X4),X0) )
            | ~ in(X3,X2) )
          & ( ? [X5] :
                ( in(X5,X1)
                & in(ordered_pair(X3,X5),X0) )
            | in(X3,X2) ) )
     => ( ( ! [X4] :
              ( ~ in(X4,X1)
              | ~ in(ordered_pair(sK0(X0,X1,X2),X4),X0) )
          | ~ in(sK0(X0,X1,X2),X2) )
        & ( ? [X5] :
              ( in(X5,X1)
              & in(ordered_pair(sK0(X0,X1,X2),X5),X0) )
          | in(sK0(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f73,plain,
    ! [X0,X1,X2] :
      ( ? [X5] :
          ( in(X5,X1)
          & in(ordered_pair(sK0(X0,X1,X2),X5),X0) )
     => ( in(sK1(X0,X1,X2),X1)
        & in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f74,plain,
    ! [X0,X1,X6] :
      ( ? [X8] :
          ( in(X8,X1)
          & in(ordered_pair(X6,X8),X0) )
     => ( in(sK2(X0,X1,X6),X1)
        & in(ordered_pair(X6,sK2(X0,X1,X6)),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f75,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( relation_inverse_image(X0,X1) = X2
            | ( ( ! [X4] :
                    ( ~ in(X4,X1)
                    | ~ in(ordered_pair(sK0(X0,X1,X2),X4),X0) )
                | ~ in(sK0(X0,X1,X2),X2) )
              & ( ( in(sK1(X0,X1,X2),X1)
                  & in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X0) )
                | in(sK0(X0,X1,X2),X2) ) ) )
          & ( ! [X6] :
                ( ( in(X6,X2)
                  | ! [X7] :
                      ( ~ in(X7,X1)
                      | ~ in(ordered_pair(X6,X7),X0) ) )
                & ( ( in(sK2(X0,X1,X6),X1)
                    & in(ordered_pair(X6,sK2(X0,X1,X6)),X0) )
                  | ~ in(X6,X2) ) )
            | relation_inverse_image(X0,X1) != X2 ) )
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f71,f74,f73,f72]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | X0 != X2 )
            & ( X0 = X2
              | ~ in(X2,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(nnf_transformation,[],[f7]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(rectify,[],[f76]) ).

fof(f78,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( X0 != X2
            | ~ in(X2,X1) )
          & ( X0 = X2
            | in(X2,X1) ) )
     => ( ( sK3(X0,X1) != X0
          | ~ in(sK3(X0,X1),X1) )
        & ( sK3(X0,X1) = X0
          | in(sK3(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f79,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ( ( sK3(X0,X1) != X0
            | ~ in(sK3(X0,X1),X1) )
          & ( sK3(X0,X1) = X0
            | in(sK3(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f77,f78]) ).

fof(f80,plain,
    ! [X0] :
      ( ( empty_set = X0
        | ? [X1] : in(X1,X0) )
      & ( ! [X1] : ~ in(X1,X0)
        | empty_set != X0 ) ),
    inference(nnf_transformation,[],[f8]) ).

fof(f81,plain,
    ! [X0] :
      ( ( empty_set = X0
        | ? [X1] : in(X1,X0) )
      & ( ! [X2] : ~ in(X2,X0)
        | empty_set != X0 ) ),
    inference(rectify,[],[f80]) ).

fof(f82,plain,
    ! [X0] :
      ( ? [X1] : in(X1,X0)
     => in(sK4(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f83,plain,
    ! [X0] :
      ( ( empty_set = X0
        | in(sK4(X0),X0) )
      & ( ! [X2] : ~ in(X2,X0)
        | empty_set != X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f81,f82]) ).

fof(f84,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_rng(X0) = X1
            | ? [X2] :
                ( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
                  | ~ in(X2,X1) )
                & ( ? [X3] : in(ordered_pair(X3,X2),X0)
                  | in(X2,X1) ) ) )
          & ( ! [X2] :
                ( ( in(X2,X1)
                  | ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
                & ( ? [X3] : in(ordered_pair(X3,X2),X0)
                  | ~ in(X2,X1) ) )
            | relation_rng(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f54]) ).

fof(f85,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_rng(X0) = X1
            | ? [X2] :
                ( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
                  | ~ in(X2,X1) )
                & ( ? [X4] : in(ordered_pair(X4,X2),X0)
                  | in(X2,X1) ) ) )
          & ( ! [X5] :
                ( ( in(X5,X1)
                  | ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
                & ( ? [X7] : in(ordered_pair(X7,X5),X0)
                  | ~ in(X5,X1) ) )
            | relation_rng(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(rectify,[],[f84]) ).

fof(f86,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
            | ~ in(X2,X1) )
          & ( ? [X4] : in(ordered_pair(X4,X2),X0)
            | in(X2,X1) ) )
     => ( ( ! [X3] : ~ in(ordered_pair(X3,sK5(X0,X1)),X0)
          | ~ in(sK5(X0,X1),X1) )
        & ( ? [X4] : in(ordered_pair(X4,sK5(X0,X1)),X0)
          | in(sK5(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f87,plain,
    ! [X0,X1] :
      ( ? [X4] : in(ordered_pair(X4,sK5(X0,X1)),X0)
     => in(ordered_pair(sK6(X0,X1),sK5(X0,X1)),X0) ),
    introduced(choice_axiom,[]) ).

fof(f88,plain,
    ! [X0,X5] :
      ( ? [X7] : in(ordered_pair(X7,X5),X0)
     => in(ordered_pair(sK7(X0,X5),X5),X0) ),
    introduced(choice_axiom,[]) ).

fof(f89,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_rng(X0) = X1
            | ( ( ! [X3] : ~ in(ordered_pair(X3,sK5(X0,X1)),X0)
                | ~ in(sK5(X0,X1),X1) )
              & ( in(ordered_pair(sK6(X0,X1),sK5(X0,X1)),X0)
                | in(sK5(X0,X1),X1) ) ) )
          & ( ! [X5] :
                ( ( in(X5,X1)
                  | ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
                & ( in(ordered_pair(sK7(X0,X5),X5),X0)
                  | ~ in(X5,X1) ) )
            | relation_rng(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f85,f88,f87,f86]) ).

fof(f112,plain,
    ? [X0,X1] :
      ( ( empty_set = relation_inverse_image(X1,singleton(X0))
        | ~ in(X0,relation_rng(X1)) )
      & ( empty_set != relation_inverse_image(X1,singleton(X0))
        | in(X0,relation_rng(X1)) )
      & relation(X1) ),
    inference(nnf_transformation,[],[f59]) ).

fof(f113,plain,
    ? [X0,X1] :
      ( ( empty_set = relation_inverse_image(X1,singleton(X0))
        | ~ in(X0,relation_rng(X1)) )
      & ( empty_set != relation_inverse_image(X1,singleton(X0))
        | in(X0,relation_rng(X1)) )
      & relation(X1) ),
    inference(flattening,[],[f112]) ).

fof(f114,plain,
    ( ? [X0,X1] :
        ( ( empty_set = relation_inverse_image(X1,singleton(X0))
          | ~ in(X0,relation_rng(X1)) )
        & ( empty_set != relation_inverse_image(X1,singleton(X0))
          | in(X0,relation_rng(X1)) )
        & relation(X1) )
   => ( ( empty_set = relation_inverse_image(sK20,singleton(sK19))
        | ~ in(sK19,relation_rng(sK20)) )
      & ( empty_set != relation_inverse_image(sK20,singleton(sK19))
        | in(sK19,relation_rng(sK20)) )
      & relation(sK20) ) ),
    introduced(choice_axiom,[]) ).

fof(f115,plain,
    ( ( empty_set = relation_inverse_image(sK20,singleton(sK19))
      | ~ in(sK19,relation_rng(sK20)) )
    & ( empty_set != relation_inverse_image(sK20,singleton(sK19))
      | in(sK19,relation_rng(sK20)) )
    & relation(sK20) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK19,sK20])],[f113,f114]) ).

fof(f118,plain,
    ! [X0] :
      ( relation(X0)
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f50]) ).

fof(f122,plain,
    ! [X2,X0,X1,X6] :
      ( in(ordered_pair(X6,sK2(X0,X1,X6)),X0)
      | ~ in(X6,X2)
      | relation_inverse_image(X0,X1) != X2
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f124,plain,
    ! [X2,X0,X1,X6,X7] :
      ( in(X6,X2)
      | ~ in(X7,X1)
      | ~ in(ordered_pair(X6,X7),X0)
      | relation_inverse_image(X0,X1) != X2
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f125,plain,
    ! [X2,X0,X1] :
      ( relation_inverse_image(X0,X1) = X2
      | in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X0)
      | in(sK0(X0,X1,X2),X2)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f126,plain,
    ! [X2,X0,X1] :
      ( relation_inverse_image(X0,X1) = X2
      | in(sK1(X0,X1,X2),X1)
      | in(sK0(X0,X1,X2),X2)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f128,plain,
    ! [X3,X0,X1] :
      ( X0 = X3
      | ~ in(X3,X1)
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f79]) ).

fof(f129,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | X0 != X3
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f79]) ).

fof(f130,plain,
    ! [X0,X1] :
      ( singleton(X0) = X1
      | sK3(X0,X1) = X0
      | in(sK3(X0,X1),X1) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f133,plain,
    ! [X0] :
      ( empty_set = X0
      | in(sK4(X0),X0) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f134,plain,
    ! [X0,X1,X5] :
      ( in(ordered_pair(sK7(X0,X5),X5),X0)
      | ~ in(X5,X1)
      | relation_rng(X0) != X1
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f135,plain,
    ! [X0,X1,X6,X5] :
      ( in(X5,X1)
      | ~ in(ordered_pair(X6,X5),X0)
      | relation_rng(X0) != X1
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f138,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    inference(cnf_transformation,[],[f10]) ).

fof(f145,plain,
    ! [X0] : ~ empty(singleton(X0)),
    inference(cnf_transformation,[],[f16]) ).

fof(f147,plain,
    empty(empty_set),
    inference(cnf_transformation,[],[f18]) ).

fof(f149,plain,
    ! [X0] :
      ( ~ empty(relation_rng(X0))
      | ~ relation(X0)
      | empty(X0) ),
    inference(cnf_transformation,[],[f56]) ).

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

fof(f170,plain,
    ! [X0] : subset(X0,X0),
    inference(cnf_transformation,[],[f42]) ).

fof(f171,plain,
    relation(sK20),
    inference(cnf_transformation,[],[f115]) ).

fof(f172,plain,
    ( empty_set != relation_inverse_image(sK20,singleton(sK19))
    | in(sK19,relation_rng(sK20)) ),
    inference(cnf_transformation,[],[f115]) ).

fof(f173,plain,
    ( empty_set = relation_inverse_image(sK20,singleton(sK19))
    | ~ in(sK19,relation_rng(sK20)) ),
    inference(cnf_transformation,[],[f115]) ).

fof(f175,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f176,plain,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f177,plain,
    ! [X2,X0,X1] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f179,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f180,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f183,plain,
    ! [X2,X0,X1] :
      ( relation_inverse_image(X0,X1) = X2
      | in(unordered_pair(unordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),singleton(sK0(X0,X1,X2))),X0)
      | in(sK0(X0,X1,X2),X2)
      | ~ relation(X0) ),
    inference(definition_unfolding,[],[f125,f138]) ).

fof(f184,plain,
    ! [X2,X0,X1,X6,X7] :
      ( in(X6,X2)
      | ~ in(X7,X1)
      | ~ in(unordered_pair(unordered_pair(X6,X7),singleton(X6)),X0)
      | relation_inverse_image(X0,X1) != X2
      | ~ relation(X0) ),
    inference(definition_unfolding,[],[f124,f138]) ).

fof(f185,plain,
    ! [X2,X0,X1,X6] :
      ( in(unordered_pair(unordered_pair(X6,sK2(X0,X1,X6)),singleton(X6)),X0)
      | ~ in(X6,X2)
      | relation_inverse_image(X0,X1) != X2
      | ~ relation(X0) ),
    inference(definition_unfolding,[],[f122,f138]) ).

fof(f188,plain,
    ! [X0,X1,X6,X5] :
      ( in(X5,X1)
      | ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
      | relation_rng(X0) != X1
      | ~ relation(X0) ),
    inference(definition_unfolding,[],[f135,f138]) ).

fof(f189,plain,
    ! [X0,X1,X5] :
      ( in(unordered_pair(unordered_pair(sK7(X0,X5),X5),singleton(sK7(X0,X5))),X0)
      | ~ in(X5,X1)
      | relation_rng(X0) != X1
      | ~ relation(X0) ),
    inference(definition_unfolding,[],[f134,f138]) ).

fof(f191,plain,
    ! [X0,X1,X6,X7] :
      ( in(X6,relation_inverse_image(X0,X1))
      | ~ in(X7,X1)
      | ~ in(unordered_pair(unordered_pair(X6,X7),singleton(X6)),X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f184]) ).

fof(f193,plain,
    ! [X0,X1,X6] :
      ( in(unordered_pair(unordered_pair(X6,sK2(X0,X1,X6)),singleton(X6)),X0)
      | ~ in(X6,relation_inverse_image(X0,X1))
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f185]) ).

fof(f194,plain,
    ! [X3,X1] :
      ( in(X3,X1)
      | singleton(X3) != X1 ),
    inference(equality_resolution,[],[f129]) ).

fof(f195,plain,
    ! [X3] : in(X3,singleton(X3)),
    inference(equality_resolution,[],[f194]) ).

fof(f196,plain,
    ! [X3,X0] :
      ( X0 = X3
      | ~ in(X3,singleton(X0)) ),
    inference(equality_resolution,[],[f128]) ).

fof(f198,plain,
    ! [X0,X6,X5] :
      ( in(X5,relation_rng(X0))
      | ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f188]) ).

fof(f199,plain,
    ! [X0,X5] :
      ( in(unordered_pair(unordered_pair(sK7(X0,X5),X5),singleton(sK7(X0,X5))),X0)
      | ~ in(X5,relation_rng(X0))
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f189]) ).

cnf(c_51,plain,
    ( ~ empty(X0)
    | relation(X0) ),
    inference(cnf_transformation,[],[f118]) ).

cnf(c_54,plain,
    ( ~ relation(X0)
    | relation_inverse_image(X0,X1) = X2
    | in(sK0(X0,X1,X2),X2)
    | in(sK1(X0,X1,X2),X1) ),
    inference(cnf_transformation,[],[f126]) ).

cnf(c_55,plain,
    ( ~ relation(X0)
    | relation_inverse_image(X0,X1) = X2
    | in(unordered_pair(unordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),singleton(sK0(X0,X1,X2))),X0)
    | in(sK0(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f183]) ).

cnf(c_56,plain,
    ( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
    | ~ in(X1,X3)
    | ~ relation(X2)
    | in(X0,relation_inverse_image(X2,X3)) ),
    inference(cnf_transformation,[],[f191]) ).

cnf(c_58,plain,
    ( ~ in(X0,relation_inverse_image(X1,X2))
    | ~ relation(X1)
    | in(unordered_pair(unordered_pair(X0,sK2(X1,X2,X0)),singleton(X0)),X1) ),
    inference(cnf_transformation,[],[f193]) ).

cnf(c_60,plain,
    ( sK3(X0,X1) = X0
    | singleton(X0) = X1
    | in(sK3(X0,X1),X1) ),
    inference(cnf_transformation,[],[f130]) ).

cnf(c_61,plain,
    in(X0,singleton(X0)),
    inference(cnf_transformation,[],[f195]) ).

cnf(c_62,plain,
    ( ~ in(X0,singleton(X1))
    | X0 = X1 ),
    inference(cnf_transformation,[],[f196]) ).

cnf(c_63,plain,
    ( X0 = empty_set
    | in(sK4(X0),X0) ),
    inference(cnf_transformation,[],[f133]) ).

cnf(c_67,plain,
    ( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
    | ~ relation(X2)
    | in(X1,relation_rng(X2)) ),
    inference(cnf_transformation,[],[f198]) ).

cnf(c_68,plain,
    ( ~ in(X0,relation_rng(X1))
    | ~ relation(X1)
    | in(unordered_pair(unordered_pair(sK7(X1,X0),X0),singleton(sK7(X1,X0))),X1) ),
    inference(cnf_transformation,[],[f199]) ).

cnf(c_75,plain,
    ~ empty(singleton(X0)),
    inference(cnf_transformation,[],[f145]) ).

cnf(c_78,plain,
    empty(empty_set),
    inference(cnf_transformation,[],[f147]) ).

cnf(c_79,plain,
    ( ~ empty(relation_rng(X0))
    | ~ relation(X0)
    | empty(X0) ),
    inference(cnf_transformation,[],[f149]) ).

cnf(c_81,plain,
    ( ~ empty(X0)
    | empty(relation_rng(X0)) ),
    inference(cnf_transformation,[],[f150]) ).

cnf(c_100,plain,
    subset(X0,X0),
    inference(cnf_transformation,[],[f170]) ).

cnf(c_101,negated_conjecture,
    ( ~ in(sK19,relation_rng(sK20))
    | relation_inverse_image(sK20,singleton(sK19)) = empty_set ),
    inference(cnf_transformation,[],[f173]) ).

cnf(c_102,negated_conjecture,
    ( relation_inverse_image(sK20,singleton(sK19)) != empty_set
    | in(sK19,relation_rng(sK20)) ),
    inference(cnf_transformation,[],[f172]) ).

cnf(c_103,negated_conjecture,
    relation(sK20),
    inference(cnf_transformation,[],[f171]) ).

cnf(c_105,plain,
    ( ~ element(X0,X1)
    | in(X0,X1)
    | empty(X1) ),
    inference(cnf_transformation,[],[f175]) ).

cnf(c_106,plain,
    ( ~ subset(X0,X1)
    | element(X0,powerset(X1)) ),
    inference(cnf_transformation,[],[f176]) ).

cnf(c_107,plain,
    ( ~ element(X0,powerset(X1))
    | ~ in(X2,X0)
    | element(X2,X1) ),
    inference(cnf_transformation,[],[f177]) ).

cnf(c_109,plain,
    ( ~ empty(X0)
    | X0 = empty_set ),
    inference(cnf_transformation,[],[f179]) ).

cnf(c_110,plain,
    ( ~ in(X0,X1)
    | ~ empty(X1) ),
    inference(cnf_transformation,[],[f180]) ).

cnf(c_163,plain,
    X0 = X0,
    theory(equality) ).

cnf(c_165,plain,
    ( X0 != X1
    | X2 != X1
    | X2 = X0 ),
    theory(equality) ).

cnf(c_166,plain,
    ( X0 != X1
    | X2 != X3
    | ~ in(X1,X3)
    | in(X0,X2) ),
    theory(equality) ).

cnf(c_167,plain,
    ( X0 != X1
    | ~ empty(X1)
    | empty(X0) ),
    theory(equality) ).

cnf(c_173,plain,
    ( X0 != X1
    | X2 != X3
    | ~ element(X1,X3)
    | element(X0,X2) ),
    theory(equality) ).

cnf(c_196,plain,
    ( singleton(X0) != X1
    | ~ empty(X1)
    | empty(singleton(X0)) ),
    inference(instantiation,[status(thm)],[c_167]) ).

cnf(c_211,plain,
    ( ~ relation(sK20)
    | relation_inverse_image(sK20,singleton(sK19)) = empty_set
    | in(sK1(sK20,singleton(sK19),empty_set),singleton(sK19))
    | in(sK0(sK20,singleton(sK19),empty_set),empty_set) ),
    inference(instantiation,[status(thm)],[c_54]) ).

cnf(c_240,plain,
    ( ~ relation(sK20)
    | relation_inverse_image(sK20,singleton(sK19)) = empty_set
    | in(unordered_pair(unordered_pair(sK0(sK20,singleton(sK19),empty_set),sK1(sK20,singleton(sK19),empty_set)),singleton(sK0(sK20,singleton(sK19),empty_set))),sK20)
    | in(sK0(sK20,singleton(sK19),empty_set),empty_set) ),
    inference(instantiation,[status(thm)],[c_55]) ).

cnf(c_280,plain,
    ( ~ in(sK19,relation_rng(sK20))
    | ~ empty(relation_rng(sK20)) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_286,plain,
    ( ~ in(sK19,relation_rng(sK20))
    | ~ relation(sK20)
    | in(unordered_pair(unordered_pair(sK7(sK20,sK19),sK19),singleton(sK7(sK20,sK19))),sK20) ),
    inference(instantiation,[status(thm)],[c_68]) ).

cnf(c_621,plain,
    ( relation_inverse_image(sK20,singleton(sK19)) != X0
    | ~ empty(X0)
    | empty(relation_inverse_image(sK20,singleton(sK19))) ),
    inference(instantiation,[status(thm)],[c_167]) ).

cnf(c_623,plain,
    ( relation_inverse_image(sK20,singleton(sK19)) != empty_set
    | ~ empty(empty_set)
    | empty(relation_inverse_image(sK20,singleton(sK19))) ),
    inference(instantiation,[status(thm)],[c_621]) ).

cnf(c_676,plain,
    ( ~ empty(relation_inverse_image(sK20,singleton(sK19)))
    | in(sK19,relation_rng(sK20)) ),
    inference(resolution,[status(thm)],[c_109,c_102]) ).

cnf(c_684,plain,
    ( ~ element(sK19,relation_rng(sK20))
    | in(sK19,relation_rng(sK20))
    | empty(relation_rng(sK20)) ),
    inference(instantiation,[status(thm)],[c_105]) ).

cnf(c_697,plain,
    ( ~ empty(sK20)
    | empty(relation_rng(sK20)) ),
    inference(instantiation,[status(thm)],[c_81]) ).

cnf(c_717,plain,
    ( ~ in(sK0(sK20,singleton(sK19),empty_set),empty_set)
    | ~ empty(empty_set) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_747,plain,
    ( in(sK4(relation_inverse_image(sK20,singleton(sK19))),relation_inverse_image(sK20,singleton(sK19)))
    | in(sK19,relation_rng(sK20)) ),
    inference(resolution,[status(thm)],[c_63,c_102]) ).

cnf(c_1496,plain,
    ( X0 != empty_set
    | ~ empty(X1)
    | X1 = X0 ),
    inference(resolution,[status(thm)],[c_165,c_109]) ).

cnf(c_1729,plain,
    ( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
    | ~ in(X1,singleton(X3))
    | ~ relation(X2)
    | in(X0,relation_inverse_image(X2,singleton(X3))) ),
    inference(instantiation,[status(thm)],[c_56]) ).

cnf(c_2874,plain,
    ( ~ in(unordered_pair(unordered_pair(sK0(sK20,singleton(sK19),empty_set),sK1(sK20,singleton(sK19),empty_set)),singleton(sK0(sK20,singleton(sK19),empty_set))),sK20)
    | ~ relation(sK20)
    | in(sK1(sK20,singleton(sK19),empty_set),relation_rng(sK20)) ),
    inference(instantiation,[status(thm)],[c_67]) ).

cnf(c_2969,plain,
    ( ~ in(X0,relation_inverse_image(sK20,singleton(sK19)))
    | ~ empty(relation_inverse_image(sK20,singleton(sK19))) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_3073,plain,
    ( ~ in(X0,relation_inverse_image(X1,X2))
    | ~ empty(X1)
    | ~ relation(X1) ),
    inference(resolution,[status(thm)],[c_58,c_110]) ).

cnf(c_3149,plain,
    ( ~ subset(relation_rng(sK20),X0)
    | element(relation_rng(sK20),powerset(X0)) ),
    inference(instantiation,[status(thm)],[c_106]) ).

cnf(c_3159,plain,
    ( ~ in(X0,singleton(sK19))
    | X0 = sK19 ),
    inference(instantiation,[status(thm)],[c_62]) ).

cnf(c_3177,plain,
    sK19 = sK19,
    inference(instantiation,[status(thm)],[c_163]) ).

cnf(c_3277,plain,
    ( ~ empty(relation_rng(sK20))
    | ~ relation(sK20)
    | empty(sK20) ),
    inference(instantiation,[status(thm)],[c_79]) ).

cnf(c_7644,plain,
    ( ~ in(unordered_pair(unordered_pair(sK7(sK20,sK19),sK19),singleton(sK7(sK20,sK19))),sK20)
    | ~ in(sK19,singleton(X0))
    | ~ relation(sK20)
    | in(sK7(sK20,sK19),relation_inverse_image(sK20,singleton(X0))) ),
    inference(instantiation,[status(thm)],[c_1729]) ).

cnf(c_9075,plain,
    ( ~ subset(relation_rng(sK20),relation_rng(sK20))
    | element(relation_rng(sK20),powerset(relation_rng(sK20))) ),
    inference(instantiation,[status(thm)],[c_3149]) ).

cnf(c_9076,plain,
    subset(relation_rng(sK20),relation_rng(sK20)),
    inference(instantiation,[status(thm)],[c_100]) ).

cnf(c_9088,plain,
    ( ~ in(sK1(sK20,singleton(sK19),empty_set),singleton(sK19))
    | sK1(sK20,singleton(sK19),empty_set) = sK19 ),
    inference(instantiation,[status(thm)],[c_3159]) ).

cnf(c_9118,plain,
    ( sK3(relation_rng(sK20),X0) = relation_rng(sK20)
    | singleton(relation_rng(sK20)) = X0
    | in(sK3(relation_rng(sK20),X0),X0) ),
    inference(instantiation,[status(thm)],[c_60]) ).

cnf(c_9120,plain,
    ( sK3(relation_rng(sK20),empty_set) = relation_rng(sK20)
    | singleton(relation_rng(sK20)) = empty_set
    | in(sK3(relation_rng(sK20),empty_set),empty_set) ),
    inference(instantiation,[status(thm)],[c_9118]) ).

cnf(c_9150,plain,
    ( ~ in(unordered_pair(unordered_pair(sK7(sK20,sK19),sK19),singleton(sK7(sK20,sK19))),sK20)
    | ~ in(sK19,singleton(sK19))
    | ~ relation(sK20)
    | in(sK7(sK20,sK19),relation_inverse_image(sK20,singleton(sK19))) ),
    inference(instantiation,[status(thm)],[c_7644]) ).

cnf(c_9151,plain,
    in(sK19,singleton(sK19)),
    inference(instantiation,[status(thm)],[c_61]) ).

cnf(c_9323,plain,
    ( X0 != X1
    | sK19 != X1
    | sK19 = X0 ),
    inference(instantiation,[status(thm)],[c_165]) ).

cnf(c_10342,plain,
    ( ~ empty(X0)
    | X0 = X1
    | in(sK4(X1),X1) ),
    inference(resolution,[status(thm)],[c_1496,c_63]) ).

cnf(c_12271,plain,
    ( ~ in(X0,relation_inverse_image(X1,X2))
    | ~ empty(X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_3073,c_51]) ).

cnf(c_12326,plain,
    ( ~ empty(sK20)
    | in(sK19,relation_rng(sK20)) ),
    inference(resolution,[status(thm)],[c_12271,c_747]) ).

cnf(c_12490,plain,
    ~ empty(sK20),
    inference(global_subsumption_just,[status(thm)],[c_12326,c_280,c_697,c_12326]) ).

cnf(c_14841,plain,
    ( ~ in(sK7(sK20,sK19),relation_inverse_image(sK20,singleton(sK19)))
    | ~ empty(relation_inverse_image(sK20,singleton(sK19))) ),
    inference(instantiation,[status(thm)],[c_2969]) ).

cnf(c_16957,plain,
    ( X0 != sK19
    | sK19 != sK19
    | sK19 = X0 ),
    inference(instantiation,[status(thm)],[c_9323]) ).

cnf(c_22172,plain,
    ( sK1(sK20,singleton(sK19),empty_set) != sK19
    | sK19 != sK19
    | sK19 = sK1(sK20,singleton(sK19),empty_set) ),
    inference(instantiation,[status(thm)],[c_16957]) ).

cnf(c_23183,plain,
    ( singleton(relation_rng(sK20)) != X0
    | ~ empty(X0)
    | empty(singleton(relation_rng(sK20))) ),
    inference(instantiation,[status(thm)],[c_196]) ).

cnf(c_23184,plain,
    ( singleton(relation_rng(sK20)) != empty_set
    | ~ empty(empty_set)
    | empty(singleton(relation_rng(sK20))) ),
    inference(instantiation,[status(thm)],[c_23183]) ).

cnf(c_60615,plain,
    ( ~ in(sK3(relation_rng(sK20),X0),X0)
    | ~ empty(X0) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_60616,plain,
    ( ~ in(sK3(relation_rng(sK20),empty_set),empty_set)
    | ~ empty(empty_set) ),
    inference(instantiation,[status(thm)],[c_60615]) ).

cnf(c_135540,plain,
    ( X0 != sK1(sK20,singleton(sK19),empty_set)
    | X1 != relation_rng(sK20)
    | ~ in(sK1(sK20,singleton(sK19),empty_set),relation_rng(sK20))
    | in(X0,X1) ),
    inference(instantiation,[status(thm)],[c_166]) ).

cnf(c_136115,plain,
    powerset(X0) = powerset(X0),
    inference(instantiation,[status(thm)],[c_163]) ).

cnf(c_137144,plain,
    ( sK3(relation_rng(sK20),X0) != relation_rng(sK20)
    | X1 != sK1(sK20,singleton(sK19),empty_set)
    | ~ in(sK1(sK20,singleton(sK19),empty_set),relation_rng(sK20))
    | in(X1,sK3(relation_rng(sK20),X0)) ),
    inference(instantiation,[status(thm)],[c_135540]) ).

cnf(c_144758,plain,
    ( ~ element(X0,powerset(relation_rng(sK20)))
    | ~ in(sK19,X0)
    | element(sK19,relation_rng(sK20)) ),
    inference(instantiation,[status(thm)],[c_107]) ).

cnf(c_149166,plain,
    ( powerset(relation_rng(sK20)) != X0
    | X1 != X2
    | ~ element(X2,X0)
    | element(X1,powerset(relation_rng(sK20))) ),
    inference(instantiation,[status(thm)],[c_173]) ).

cnf(c_153831,plain,
    ( powerset(relation_rng(sK20)) != powerset(relation_rng(sK20))
    | X0 != X1
    | ~ element(X1,powerset(relation_rng(sK20)))
    | element(X0,powerset(relation_rng(sK20))) ),
    inference(instantiation,[status(thm)],[c_149166]) ).

cnf(c_153833,plain,
    powerset(relation_rng(sK20)) = powerset(relation_rng(sK20)),
    inference(instantiation,[status(thm)],[c_136115]) ).

cnf(c_154570,plain,
    ( ~ empty(relation_inverse_image(sK20,singleton(sK19)))
    | in(sK4(empty_set),empty_set)
    | in(sK19,relation_rng(sK20)) ),
    inference(resolution,[status(thm)],[c_10342,c_102]) ).

cnf(c_157451,plain,
    ~ empty(relation_inverse_image(sK20,singleton(sK19))),
    inference(global_subsumption_just,[status(thm)],[c_154570,c_103,c_286,c_676,c_9150,c_9151,c_14841]) ).

cnf(c_157593,plain,
    ( ~ element(sK3(relation_rng(sK20),X0),powerset(relation_rng(sK20)))
    | ~ in(sK19,sK3(relation_rng(sK20),X0))
    | element(sK19,relation_rng(sK20)) ),
    inference(instantiation,[status(thm)],[c_144758]) ).

cnf(c_157594,plain,
    ( sK3(relation_rng(sK20),X0) != relation_rng(sK20)
    | sK19 != sK1(sK20,singleton(sK19),empty_set)
    | ~ in(sK1(sK20,singleton(sK19),empty_set),relation_rng(sK20))
    | in(sK19,sK3(relation_rng(sK20),X0)) ),
    inference(instantiation,[status(thm)],[c_137144]) ).

cnf(c_157595,plain,
    ( ~ element(sK3(relation_rng(sK20),empty_set),powerset(relation_rng(sK20)))
    | ~ in(sK19,sK3(relation_rng(sK20),empty_set))
    | element(sK19,relation_rng(sK20)) ),
    inference(instantiation,[status(thm)],[c_157593]) ).

cnf(c_157596,plain,
    ( sK3(relation_rng(sK20),empty_set) != relation_rng(sK20)
    | sK19 != sK1(sK20,singleton(sK19),empty_set)
    | ~ in(sK1(sK20,singleton(sK19),empty_set),relation_rng(sK20))
    | in(sK19,sK3(relation_rng(sK20),empty_set)) ),
    inference(instantiation,[status(thm)],[c_157594]) ).

cnf(c_164494,plain,
    ( sK3(relation_rng(sK20),X0) != X1
    | powerset(relation_rng(sK20)) != powerset(relation_rng(sK20))
    | ~ element(X1,powerset(relation_rng(sK20)))
    | element(sK3(relation_rng(sK20),X0),powerset(relation_rng(sK20))) ),
    inference(instantiation,[status(thm)],[c_153831]) ).

cnf(c_170664,plain,
    ( sK3(relation_rng(sK20),X0) != relation_rng(sK20)
    | powerset(relation_rng(sK20)) != powerset(relation_rng(sK20))
    | ~ element(relation_rng(sK20),powerset(relation_rng(sK20)))
    | element(sK3(relation_rng(sK20),X0),powerset(relation_rng(sK20))) ),
    inference(instantiation,[status(thm)],[c_164494]) ).

cnf(c_170665,plain,
    ( sK3(relation_rng(sK20),empty_set) != relation_rng(sK20)
    | powerset(relation_rng(sK20)) != powerset(relation_rng(sK20))
    | ~ element(relation_rng(sK20),powerset(relation_rng(sK20)))
    | element(sK3(relation_rng(sK20),empty_set),powerset(relation_rng(sK20))) ),
    inference(instantiation,[status(thm)],[c_170664]) ).

cnf(c_223776,plain,
    ~ empty(singleton(relation_rng(sK20))),
    inference(instantiation,[status(thm)],[c_75]) ).

cnf(c_223777,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_223776,c_170665,c_157596,c_157595,c_157451,c_153833,c_60616,c_23184,c_22172,c_12490,c_9120,c_9088,c_9076,c_9075,c_3277,c_3177,c_2874,c_717,c_684,c_623,c_240,c_211,c_101,c_78,c_103]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU061+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n015.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 : Wed Aug 23 18:38:35 EDT 2023
% 0.13/0.36  % CPUTime  : 
% 0.20/0.50  Running first-order theorem proving
% 0.20/0.50  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 109.60/15.37  % SZS status Started for theBenchmark.p
% 109.60/15.37  % SZS status Theorem for theBenchmark.p
% 109.60/15.37  
% 109.60/15.37  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 109.60/15.37  
% 109.60/15.37  ------  iProver source info
% 109.60/15.37  
% 109.60/15.37  git: date: 2023-05-31 18:12:56 +0000
% 109.60/15.37  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 109.60/15.37  git: non_committed_changes: false
% 109.60/15.37  git: last_make_outside_of_git: false
% 109.60/15.37  
% 109.60/15.37  ------ Parsing...
% 109.60/15.37  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 109.60/15.37  
% 109.60/15.37  ------ Preprocessing... sf_s  rm: 6 0s  sf_e  sf_s  rm: 2 0s  sf_e 
% 109.60/15.37  
% 109.60/15.37  ------ Preprocessing...
% 109.60/15.37  
% 109.60/15.37  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 109.60/15.37  ------ Proving...
% 109.60/15.37  ------ Problem Properties 
% 109.60/15.37  
% 109.60/15.37  
% 109.60/15.37  clauses                                 56
% 109.60/15.37  conjectures                             3
% 109.60/15.37  EPR                                     23
% 109.60/15.37  Horn                                    49
% 109.60/15.37  unary                                   25
% 109.60/15.37  binary                                  14
% 109.60/15.37  lits                                    111
% 109.60/15.37  lits eq                                 16
% 109.60/15.37  fd_pure                                 0
% 109.60/15.37  fd_pseudo                               0
% 109.60/15.37  fd_cond                                 2
% 109.60/15.37  fd_pseudo_cond                          8
% 109.60/15.37  AC symbols                              0
% 109.60/15.37  
% 109.60/15.37  ------ Input Options Time Limit: Unbounded
% 109.60/15.37  
% 109.60/15.37  
% 109.60/15.37  ------ 
% 109.60/15.37  Current options:
% 109.60/15.37  ------ 
% 109.60/15.37  
% 109.60/15.37  
% 109.60/15.37  
% 109.60/15.37  
% 109.60/15.37  ------ Proving...
% 109.60/15.37  
% 109.60/15.37  
% 109.60/15.37  % SZS status Theorem for theBenchmark.p
% 109.60/15.37  
% 109.60/15.37  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 109.60/15.37  
% 109.60/15.38  
%------------------------------------------------------------------------------