TSTP Solution File: NUM397+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : NUM397+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n013.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 11:30:16 EDT 2023

% Result   : Theorem 39.02s 6.20s
% Output   : CNFRefutation 39.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   23
% Syntax   : Number of formulae    :  143 (  12 unt;   0 def)
%            Number of atoms       :  483 (  47 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  554 ( 214   ~; 224   |;  92   &)
%                                         (   8 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   13 (  11 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   2 con; 0-2 aty)
%            Number of variables   :  218 (   2 sgn; 135   !;  23   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f9,axiom,
    ! [X0] :
      ( epsilon_transitive(X0)
    <=> ! [X1] :
          ( in(X1,X0)
         => subset(X1,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).

fof(f10,axiom,
    ! [X0] :
      ( epsilon_connected(X0)
    <=> ! [X1,X2] :
          ~ ( ~ in(X2,X1)
            & X1 != X2
            & ~ in(X1,X2)
            & in(X2,X0)
            & in(X1,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_ordinal1) ).

fof(f11,axiom,
    ! [X0] :
      ( ordinal(X0)
    <=> ( epsilon_connected(X0)
        & epsilon_transitive(X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_ordinal1) ).

fof(f12,axiom,
    ! [X0,X1] :
      ( union(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> ? [X3] :
              ( in(X3,X0)
              & in(X2,X3) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).

fof(f16,axiom,
    ( ordinal(empty_set)
    & epsilon_connected(empty_set)
    & epsilon_transitive(empty_set)
    & empty(empty_set)
    & one_to_one(empty_set)
    & function(empty_set)
    & relation_empty_yielding(empty_set)
    & relation(empty_set) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_ordinal1) ).

fof(f17,axiom,
    ( relation(empty_set)
    & empty(empty_set) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).

fof(f34,axiom,
    ! [X0,X1] :
      ( ordinal(X1)
     => ( in(X0,X1)
       => ordinal(X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_ordinal1) ).

fof(f35,axiom,
    ! [X0] :
      ( ordinal(X0)
     => ! [X1] :
          ( ordinal(X1)
         => ~ ( ~ in(X1,X0)
              & X0 != X1
              & ~ in(X0,X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_ordinal1) ).

fof(f36,axiom,
    ! [X0,X1] :
      ( element(X0,X1)
     => ( in(X0,X1)
        | empty(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).

fof(f37,conjecture,
    ! [X0] :
      ( ordinal(X0)
     => ordinal(union(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_ordinal1) ).

fof(f38,negated_conjecture,
    ~ ! [X0] :
        ( ordinal(X0)
       => ordinal(union(X0)) ),
    inference(negated_conjecture,[],[f37]) ).

fof(f39,axiom,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).

fof(f40,axiom,
    ! [X0,X1,X2] :
      ( ( element(X1,powerset(X2))
        & in(X0,X1) )
     => element(X0,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).

fof(f43,axiom,
    ! [X0,X1] :
      ~ ( empty(X1)
        & in(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).

fof(f45,axiom,
    ! [X0,X1] :
      ( in(X0,X1)
     => subset(X0,union(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_zfmisc_1) ).

fof(f49,plain,
    ( ordinal(empty_set)
    & epsilon_connected(empty_set)
    & epsilon_transitive(empty_set)
    & empty(empty_set)
    & one_to_one(empty_set)
    & function(empty_set)
    & relation(empty_set) ),
    inference(pure_predicate_removal,[],[f16]) ).

fof(f52,plain,
    ( ordinal(empty_set)
    & epsilon_connected(empty_set)
    & epsilon_transitive(empty_set)
    & empty(empty_set)
    & function(empty_set)
    & relation(empty_set) ),
    inference(pure_predicate_removal,[],[f49]) ).

fof(f67,plain,
    ! [X0] :
      ( epsilon_transitive(X0)
    <=> ! [X1] :
          ( subset(X1,X0)
          | ~ in(X1,X0) ) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f68,plain,
    ! [X0] :
      ( epsilon_connected(X0)
    <=> ! [X1,X2] :
          ( in(X2,X1)
          | X1 = X2
          | in(X1,X2)
          | ~ in(X2,X0)
          | ~ in(X1,X0) ) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( ordinal(X0)
      | ~ in(X0,X1)
      | ~ ordinal(X1) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( ordinal(X0)
      | ~ in(X0,X1)
      | ~ ordinal(X1) ),
    inference(flattening,[],[f74]) ).

fof(f76,plain,
    ! [X0] :
      ( ! [X1] :
          ( in(X1,X0)
          | X0 = X1
          | in(X0,X1)
          | ~ ordinal(X1) )
      | ~ ordinal(X0) ),
    inference(ennf_transformation,[],[f35]) ).

fof(f77,plain,
    ! [X0] :
      ( ! [X1] :
          ( in(X1,X0)
          | X0 = X1
          | in(X0,X1)
          | ~ ordinal(X1) )
      | ~ ordinal(X0) ),
    inference(flattening,[],[f76]) ).

fof(f78,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(ennf_transformation,[],[f36]) ).

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

fof(f80,plain,
    ? [X0] :
      ( ~ ordinal(union(X0))
      & ordinal(X0) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f81,plain,
    ! [X0,X1,X2] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f40]) ).

fof(f82,plain,
    ! [X0,X1,X2] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(flattening,[],[f81]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f43]) ).

fof(f87,plain,
    ! [X0,X1] :
      ( subset(X0,union(X1))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f45]) ).

fof(f88,plain,
    ! [X0] :
      ( ( epsilon_transitive(X0)
        | ? [X1] :
            ( ~ subset(X1,X0)
            & in(X1,X0) ) )
      & ( ! [X1] :
            ( subset(X1,X0)
            | ~ in(X1,X0) )
        | ~ epsilon_transitive(X0) ) ),
    inference(nnf_transformation,[],[f67]) ).

fof(f89,plain,
    ! [X0] :
      ( ( epsilon_transitive(X0)
        | ? [X1] :
            ( ~ subset(X1,X0)
            & in(X1,X0) ) )
      & ( ! [X2] :
            ( subset(X2,X0)
            | ~ in(X2,X0) )
        | ~ epsilon_transitive(X0) ) ),
    inference(rectify,[],[f88]) ).

fof(f90,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ subset(X1,X0)
          & in(X1,X0) )
     => ( ~ subset(sK0(X0),X0)
        & in(sK0(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f91,plain,
    ! [X0] :
      ( ( epsilon_transitive(X0)
        | ( ~ subset(sK0(X0),X0)
          & in(sK0(X0),X0) ) )
      & ( ! [X2] :
            ( subset(X2,X0)
            | ~ in(X2,X0) )
        | ~ epsilon_transitive(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f89,f90]) ).

fof(f92,plain,
    ! [X0] :
      ( ( epsilon_connected(X0)
        | ? [X1,X2] :
            ( ~ in(X2,X1)
            & X1 != X2
            & ~ in(X1,X2)
            & in(X2,X0)
            & in(X1,X0) ) )
      & ( ! [X1,X2] :
            ( in(X2,X1)
            | X1 = X2
            | in(X1,X2)
            | ~ in(X2,X0)
            | ~ in(X1,X0) )
        | ~ epsilon_connected(X0) ) ),
    inference(nnf_transformation,[],[f68]) ).

fof(f93,plain,
    ! [X0] :
      ( ( epsilon_connected(X0)
        | ? [X1,X2] :
            ( ~ in(X2,X1)
            & X1 != X2
            & ~ in(X1,X2)
            & in(X2,X0)
            & in(X1,X0) ) )
      & ( ! [X3,X4] :
            ( in(X4,X3)
            | X3 = X4
            | in(X3,X4)
            | ~ in(X4,X0)
            | ~ in(X3,X0) )
        | ~ epsilon_connected(X0) ) ),
    inference(rectify,[],[f92]) ).

fof(f94,plain,
    ! [X0] :
      ( ? [X1,X2] :
          ( ~ in(X2,X1)
          & X1 != X2
          & ~ in(X1,X2)
          & in(X2,X0)
          & in(X1,X0) )
     => ( ~ in(sK2(X0),sK1(X0))
        & sK1(X0) != sK2(X0)
        & ~ in(sK1(X0),sK2(X0))
        & in(sK2(X0),X0)
        & in(sK1(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f95,plain,
    ! [X0] :
      ( ( epsilon_connected(X0)
        | ( ~ in(sK2(X0),sK1(X0))
          & sK1(X0) != sK2(X0)
          & ~ in(sK1(X0),sK2(X0))
          & in(sK2(X0),X0)
          & in(sK1(X0),X0) ) )
      & ( ! [X3,X4] :
            ( in(X4,X3)
            | X3 = X4
            | in(X3,X4)
            | ~ in(X4,X0)
            | ~ in(X3,X0) )
        | ~ epsilon_connected(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f93,f94]) ).

fof(f96,plain,
    ! [X0] :
      ( ( ordinal(X0)
        | ~ epsilon_connected(X0)
        | ~ epsilon_transitive(X0) )
      & ( ( epsilon_connected(X0)
          & epsilon_transitive(X0) )
        | ~ ordinal(X0) ) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f97,plain,
    ! [X0] :
      ( ( ordinal(X0)
        | ~ epsilon_connected(X0)
        | ~ epsilon_transitive(X0) )
      & ( ( epsilon_connected(X0)
          & epsilon_transitive(X0) )
        | ~ ordinal(X0) ) ),
    inference(flattening,[],[f96]) ).

fof(f98,plain,
    ! [X0,X1] :
      ( ( union(X0) = X1
        | ? [X2] :
            ( ( ! [X3] :
                  ( ~ in(X3,X0)
                  | ~ in(X2,X3) )
              | ~ in(X2,X1) )
            & ( ? [X3] :
                  ( in(X3,X0)
                  & in(X2,X3) )
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | ! [X3] :
                  ( ~ in(X3,X0)
                  | ~ in(X2,X3) ) )
            & ( ? [X3] :
                  ( in(X3,X0)
                  & in(X2,X3) )
              | ~ in(X2,X1) ) )
        | union(X0) != X1 ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f99,plain,
    ! [X0,X1] :
      ( ( union(X0) = X1
        | ? [X2] :
            ( ( ! [X3] :
                  ( ~ in(X3,X0)
                  | ~ in(X2,X3) )
              | ~ in(X2,X1) )
            & ( ? [X4] :
                  ( in(X4,X0)
                  & in(X2,X4) )
              | in(X2,X1) ) ) )
      & ( ! [X5] :
            ( ( in(X5,X1)
              | ! [X6] :
                  ( ~ in(X6,X0)
                  | ~ in(X5,X6) ) )
            & ( ? [X7] :
                  ( in(X7,X0)
                  & in(X5,X7) )
              | ~ in(X5,X1) ) )
        | union(X0) != X1 ) ),
    inference(rectify,[],[f98]) ).

fof(f100,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ! [X3] :
                ( ~ in(X3,X0)
                | ~ in(X2,X3) )
            | ~ in(X2,X1) )
          & ( ? [X4] :
                ( in(X4,X0)
                & in(X2,X4) )
            | in(X2,X1) ) )
     => ( ( ! [X3] :
              ( ~ in(X3,X0)
              | ~ in(sK3(X0,X1),X3) )
          | ~ in(sK3(X0,X1),X1) )
        & ( ? [X4] :
              ( in(X4,X0)
              & in(sK3(X0,X1),X4) )
          | in(sK3(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f101,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( in(X4,X0)
          & in(sK3(X0,X1),X4) )
     => ( in(sK4(X0,X1),X0)
        & in(sK3(X0,X1),sK4(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f102,plain,
    ! [X0,X5] :
      ( ? [X7] :
          ( in(X7,X0)
          & in(X5,X7) )
     => ( in(sK5(X0,X5),X0)
        & in(X5,sK5(X0,X5)) ) ),
    introduced(choice_axiom,[]) ).

fof(f103,plain,
    ! [X0,X1] :
      ( ( union(X0) = X1
        | ( ( ! [X3] :
                ( ~ in(X3,X0)
                | ~ in(sK3(X0,X1),X3) )
            | ~ in(sK3(X0,X1),X1) )
          & ( ( in(sK4(X0,X1),X0)
              & in(sK3(X0,X1),sK4(X0,X1)) )
            | in(sK3(X0,X1),X1) ) ) )
      & ( ! [X5] :
            ( ( in(X5,X1)
              | ! [X6] :
                  ( ~ in(X6,X0)
                  | ~ in(X5,X6) ) )
            & ( ( in(sK5(X0,X5),X0)
                & in(X5,sK5(X0,X5)) )
              | ~ in(X5,X1) ) )
        | union(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f99,f102,f101,f100]) ).

fof(f131,plain,
    ( ? [X0] :
        ( ~ ordinal(union(X0))
        & ordinal(X0) )
   => ( ~ ordinal(union(sK19))
      & ordinal(sK19) ) ),
    introduced(choice_axiom,[]) ).

fof(f132,plain,
    ( ~ ordinal(union(sK19))
    & ordinal(sK19) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f80,f131]) ).

fof(f133,plain,
    ! [X0,X1] :
      ( ( element(X0,powerset(X1))
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ~ element(X0,powerset(X1)) ) ),
    inference(nnf_transformation,[],[f39]) ).

fof(f146,plain,
    ! [X2,X0] :
      ( subset(X2,X0)
      | ~ in(X2,X0)
      | ~ epsilon_transitive(X0) ),
    inference(cnf_transformation,[],[f91]) ).

fof(f147,plain,
    ! [X0] :
      ( epsilon_transitive(X0)
      | in(sK0(X0),X0) ),
    inference(cnf_transformation,[],[f91]) ).

fof(f148,plain,
    ! [X0] :
      ( epsilon_transitive(X0)
      | ~ subset(sK0(X0),X0) ),
    inference(cnf_transformation,[],[f91]) ).

fof(f150,plain,
    ! [X0] :
      ( epsilon_connected(X0)
      | in(sK1(X0),X0) ),
    inference(cnf_transformation,[],[f95]) ).

fof(f151,plain,
    ! [X0] :
      ( epsilon_connected(X0)
      | in(sK2(X0),X0) ),
    inference(cnf_transformation,[],[f95]) ).

fof(f152,plain,
    ! [X0] :
      ( epsilon_connected(X0)
      | ~ in(sK1(X0),sK2(X0)) ),
    inference(cnf_transformation,[],[f95]) ).

fof(f153,plain,
    ! [X0] :
      ( epsilon_connected(X0)
      | sK1(X0) != sK2(X0) ),
    inference(cnf_transformation,[],[f95]) ).

fof(f154,plain,
    ! [X0] :
      ( epsilon_connected(X0)
      | ~ in(sK2(X0),sK1(X0)) ),
    inference(cnf_transformation,[],[f95]) ).

fof(f155,plain,
    ! [X0] :
      ( epsilon_transitive(X0)
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f97]) ).

fof(f157,plain,
    ! [X0] :
      ( ordinal(X0)
      | ~ epsilon_connected(X0)
      | ~ epsilon_transitive(X0) ),
    inference(cnf_transformation,[],[f97]) ).

fof(f158,plain,
    ! [X0,X1,X5] :
      ( in(X5,sK5(X0,X5))
      | ~ in(X5,X1)
      | union(X0) != X1 ),
    inference(cnf_transformation,[],[f103]) ).

fof(f159,plain,
    ! [X0,X1,X5] :
      ( in(sK5(X0,X5),X0)
      | ~ in(X5,X1)
      | union(X0) != X1 ),
    inference(cnf_transformation,[],[f103]) ).

fof(f162,plain,
    ! [X0,X1] :
      ( union(X0) = X1
      | in(sK4(X0,X1),X0)
      | in(sK3(X0,X1),X1) ),
    inference(cnf_transformation,[],[f103]) ).

fof(f173,plain,
    ordinal(empty_set),
    inference(cnf_transformation,[],[f52]) ).

fof(f174,plain,
    empty(empty_set),
    inference(cnf_transformation,[],[f17]) ).

fof(f208,plain,
    ! [X0,X1] :
      ( ordinal(X0)
      | ~ in(X0,X1)
      | ~ ordinal(X1) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f209,plain,
    ! [X0,X1] :
      ( in(X1,X0)
      | X0 = X1
      | in(X0,X1)
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f210,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f211,plain,
    ordinal(sK19),
    inference(cnf_transformation,[],[f132]) ).

fof(f212,plain,
    ~ ordinal(union(sK19)),
    inference(cnf_transformation,[],[f132]) ).

fof(f214,plain,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f133]) ).

fof(f215,plain,
    ! [X2,X0,X1] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f82]) ).

fof(f218,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f85]) ).

fof(f220,plain,
    ! [X0,X1] :
      ( subset(X0,union(X1))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f87]) ).

fof(f222,plain,
    ! [X0,X5] :
      ( in(sK5(X0,X5),X0)
      | ~ in(X5,union(X0)) ),
    inference(equality_resolution,[],[f159]) ).

fof(f223,plain,
    ! [X0,X5] :
      ( in(X5,sK5(X0,X5))
      | ~ in(X5,union(X0)) ),
    inference(equality_resolution,[],[f158]) ).

cnf(c_59,plain,
    ( ~ subset(sK0(X0),X0)
    | epsilon_transitive(X0) ),
    inference(cnf_transformation,[],[f148]) ).

cnf(c_60,plain,
    ( in(sK0(X0),X0)
    | epsilon_transitive(X0) ),
    inference(cnf_transformation,[],[f147]) ).

cnf(c_61,plain,
    ( ~ in(X0,X1)
    | ~ epsilon_transitive(X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f146]) ).

cnf(c_62,plain,
    ( ~ in(sK2(X0),sK1(X0))
    | epsilon_connected(X0) ),
    inference(cnf_transformation,[],[f154]) ).

cnf(c_63,plain,
    ( sK2(X0) != sK1(X0)
    | epsilon_connected(X0) ),
    inference(cnf_transformation,[],[f153]) ).

cnf(c_64,plain,
    ( ~ in(sK1(X0),sK2(X0))
    | epsilon_connected(X0) ),
    inference(cnf_transformation,[],[f152]) ).

cnf(c_65,plain,
    ( in(sK2(X0),X0)
    | epsilon_connected(X0) ),
    inference(cnf_transformation,[],[f151]) ).

cnf(c_66,plain,
    ( in(sK1(X0),X0)
    | epsilon_connected(X0) ),
    inference(cnf_transformation,[],[f150]) ).

cnf(c_68,plain,
    ( ~ epsilon_connected(X0)
    | ~ epsilon_transitive(X0)
    | ordinal(X0) ),
    inference(cnf_transformation,[],[f157]) ).

cnf(c_70,plain,
    ( ~ ordinal(X0)
    | epsilon_transitive(X0) ),
    inference(cnf_transformation,[],[f155]) ).

cnf(c_72,plain,
    ( union(X0) = X1
    | in(sK3(X0,X1),X1)
    | in(sK4(X0,X1),X0) ),
    inference(cnf_transformation,[],[f162]) ).

cnf(c_75,plain,
    ( ~ in(X0,union(X1))
    | in(sK5(X1,X0),X1) ),
    inference(cnf_transformation,[],[f222]) ).

cnf(c_76,plain,
    ( ~ in(X0,union(X1))
    | in(X0,sK5(X1,X0)) ),
    inference(cnf_transformation,[],[f223]) ).

cnf(c_81,plain,
    ordinal(empty_set),
    inference(cnf_transformation,[],[f173]) ).

cnf(c_88,plain,
    empty(empty_set),
    inference(cnf_transformation,[],[f174]) ).

cnf(c_121,plain,
    ( ~ in(X0,X1)
    | ~ ordinal(X1)
    | ordinal(X0) ),
    inference(cnf_transformation,[],[f208]) ).

cnf(c_122,plain,
    ( ~ ordinal(X0)
    | ~ ordinal(X1)
    | X0 = X1
    | in(X0,X1)
    | in(X1,X0) ),
    inference(cnf_transformation,[],[f209]) ).

cnf(c_123,plain,
    ( ~ element(X0,X1)
    | in(X0,X1)
    | empty(X1) ),
    inference(cnf_transformation,[],[f210]) ).

cnf(c_124,negated_conjecture,
    ~ ordinal(union(sK19)),
    inference(cnf_transformation,[],[f212]) ).

cnf(c_125,negated_conjecture,
    ordinal(sK19),
    inference(cnf_transformation,[],[f211]) ).

cnf(c_126,plain,
    ( ~ subset(X0,X1)
    | element(X0,powerset(X1)) ),
    inference(cnf_transformation,[],[f214]) ).

cnf(c_128,plain,
    ( ~ element(X0,powerset(X1))
    | ~ in(X2,X0)
    | element(X2,X1) ),
    inference(cnf_transformation,[],[f215]) ).

cnf(c_131,plain,
    ( ~ in(X0,X1)
    | ~ empty(X1) ),
    inference(cnf_transformation,[],[f218]) ).

cnf(c_133,plain,
    ( ~ in(X0,X1)
    | subset(X0,union(X1)) ),
    inference(cnf_transformation,[],[f220]) ).

cnf(c_151,plain,
    ( ~ subset(X0,X1)
    | element(X0,powerset(X1)) ),
    inference(prop_impl_just,[status(thm)],[c_126]) ).

cnf(c_331,plain,
    ( ~ in(X0,X1)
    | ~ subset(X1,X2)
    | element(X0,X2) ),
    inference(bin_hyper_res,[status(thm)],[c_128,c_151]) ).

cnf(c_2609,plain,
    X0 = X0,
    theory(equality) ).

cnf(c_2611,plain,
    ( X0 != X1
    | X2 != X1
    | X2 = X0 ),
    theory(equality) ).

cnf(c_2615,plain,
    ( X0 != X1
    | ~ ordinal(X1)
    | ordinal(X0) ),
    theory(equality) ).

cnf(c_3584,plain,
    ( ~ epsilon_connected(union(sK19))
    | ~ epsilon_transitive(union(sK19))
    | ordinal(union(sK19)) ),
    inference(instantiation,[status(thm)],[c_68]) ).

cnf(c_3585,plain,
    ( union(sK19) != X0
    | ~ ordinal(X0)
    | ordinal(union(sK19)) ),
    inference(instantiation,[status(thm)],[c_2615]) ).

cnf(c_3586,plain,
    ( union(sK19) != empty_set
    | ~ ordinal(empty_set)
    | ordinal(union(sK19)) ),
    inference(instantiation,[status(thm)],[c_3585]) ).

cnf(c_3607,plain,
    ( in(sK0(union(sK19)),union(sK19))
    | epsilon_transitive(union(sK19)) ),
    inference(instantiation,[status(thm)],[c_60]) ).

cnf(c_3608,plain,
    ( ~ subset(sK0(union(sK19)),union(sK19))
    | epsilon_transitive(union(sK19)) ),
    inference(instantiation,[status(thm)],[c_59]) ).

cnf(c_3617,plain,
    ( union(sK19) = X0
    | in(sK3(sK19,X0),X0)
    | in(sK4(sK19,X0),sK19) ),
    inference(instantiation,[status(thm)],[c_72]) ).

cnf(c_3618,plain,
    ( union(sK19) = empty_set
    | in(sK3(sK19,empty_set),empty_set)
    | in(sK4(sK19,empty_set),sK19) ),
    inference(instantiation,[status(thm)],[c_3617]) ).

cnf(c_3662,plain,
    ( in(sK1(union(sK19)),union(sK19))
    | epsilon_connected(union(sK19)) ),
    inference(instantiation,[status(thm)],[c_66]) ).

cnf(c_3663,plain,
    ( in(sK2(union(sK19)),union(sK19))
    | epsilon_connected(union(sK19)) ),
    inference(instantiation,[status(thm)],[c_65]) ).

cnf(c_3664,plain,
    ( sK2(union(sK19)) != sK1(union(sK19))
    | epsilon_connected(union(sK19)) ),
    inference(instantiation,[status(thm)],[c_63]) ).

cnf(c_3714,plain,
    ( ~ in(sK3(sK19,X0),X0)
    | ~ empty(X0) ),
    inference(instantiation,[status(thm)],[c_131]) ).

cnf(c_3719,plain,
    ( ~ in(sK3(sK19,empty_set),empty_set)
    | ~ empty(empty_set) ),
    inference(instantiation,[status(thm)],[c_3714]) ).

cnf(c_3795,plain,
    ( ~ in(sK4(sK19,X0),sK19)
    | ~ empty(sK19) ),
    inference(instantiation,[status(thm)],[c_131]) ).

cnf(c_3800,plain,
    ( ~ in(sK4(sK19,empty_set),sK19)
    | ~ empty(sK19) ),
    inference(instantiation,[status(thm)],[c_3795]) ).

cnf(c_3937,plain,
    ( ~ in(sK0(union(sK19)),union(sK19))
    | in(sK0(union(sK19)),sK5(sK19,sK0(union(sK19)))) ),
    inference(instantiation,[status(thm)],[c_76]) ).

cnf(c_4260,plain,
    ( ~ element(X0,sK19)
    | in(X0,sK19)
    | empty(sK19) ),
    inference(instantiation,[status(thm)],[c_123]) ).

cnf(c_4481,plain,
    epsilon_transitive(sK19),
    inference(superposition,[status(thm)],[c_125,c_70]) ).

cnf(c_4821,plain,
    ( ~ in(X0,union(X1))
    | ~ epsilon_transitive(X1)
    | subset(sK5(X1,X0),X1) ),
    inference(superposition,[status(thm)],[c_75,c_61]) ).

cnf(c_4822,plain,
    ( ~ in(X0,union(X1))
    | ~ ordinal(X1)
    | ordinal(sK5(X1,X0)) ),
    inference(superposition,[status(thm)],[c_75,c_121]) ).

cnf(c_4898,plain,
    ( ~ in(X0,union(X1))
    | ~ ordinal(sK5(X1,X0))
    | ordinal(X0) ),
    inference(superposition,[status(thm)],[c_76,c_121]) ).

cnf(c_7276,plain,
    ( ~ element(sK0(union(sK19)),sK19)
    | in(sK0(union(sK19)),sK19)
    | empty(sK19) ),
    inference(instantiation,[status(thm)],[c_4260]) ).

cnf(c_8413,plain,
    ( ~ in(sK1(union(sK19)),union(sK19))
    | ~ ordinal(sK5(sK19,sK1(union(sK19))))
    | ordinal(sK1(union(sK19))) ),
    inference(instantiation,[status(thm)],[c_4898]) ).

cnf(c_8415,plain,
    ( ~ in(sK1(union(sK19)),union(sK19))
    | ~ ordinal(sK19)
    | ordinal(sK5(sK19,sK1(union(sK19)))) ),
    inference(instantiation,[status(thm)],[c_4822]) ).

cnf(c_8432,plain,
    ( ~ in(sK2(union(sK19)),union(sK19))
    | ~ ordinal(sK5(sK19,sK2(union(sK19))))
    | ordinal(sK2(union(sK19))) ),
    inference(instantiation,[status(thm)],[c_4898]) ).

cnf(c_8434,plain,
    ( ~ in(sK2(union(sK19)),union(sK19))
    | ~ ordinal(sK19)
    | ordinal(sK5(sK19,sK2(union(sK19)))) ),
    inference(instantiation,[status(thm)],[c_4822]) ).

cnf(c_8479,plain,
    ( sK2(union(sK19)) != X0
    | sK1(union(sK19)) != X0
    | sK2(union(sK19)) = sK1(union(sK19)) ),
    inference(instantiation,[status(thm)],[c_2611]) ).

cnf(c_9244,plain,
    ( ~ ordinal(sK1(union(sK19)))
    | ~ ordinal(X0)
    | sK1(union(sK19)) = X0
    | in(sK1(union(sK19)),X0)
    | in(X0,sK1(union(sK19))) ),
    inference(instantiation,[status(thm)],[c_122]) ).

cnf(c_10463,plain,
    ( ~ in(X0,sK5(sK19,X0))
    | ~ subset(sK5(sK19,X0),X1)
    | element(X0,X1) ),
    inference(instantiation,[status(thm)],[c_331]) ).

cnf(c_11749,plain,
    ( ~ in(X0,sK19)
    | subset(X0,union(sK19)) ),
    inference(instantiation,[status(thm)],[c_133]) ).

cnf(c_13443,plain,
    ( ~ in(X0,sK5(sK19,X0))
    | ~ subset(sK5(sK19,X0),sK19)
    | element(X0,sK19) ),
    inference(instantiation,[status(thm)],[c_10463]) ).

cnf(c_21257,plain,
    ( ~ in(sK2(union(sK19)),sK1(union(sK19)))
    | epsilon_connected(union(sK19)) ),
    inference(instantiation,[status(thm)],[c_62]) ).

cnf(c_21633,plain,
    ( ~ ordinal(sK2(union(sK19)))
    | ~ ordinal(sK1(union(sK19)))
    | sK1(union(sK19)) = sK2(union(sK19))
    | in(sK2(union(sK19)),sK1(union(sK19)))
    | in(sK1(union(sK19)),sK2(union(sK19))) ),
    inference(instantiation,[status(thm)],[c_9244]) ).

cnf(c_26019,plain,
    ( sK2(union(sK19)) != sK2(union(sK19))
    | sK1(union(sK19)) != sK2(union(sK19))
    | sK2(union(sK19)) = sK1(union(sK19)) ),
    inference(instantiation,[status(thm)],[c_8479]) ).

cnf(c_26272,plain,
    ( ~ in(sK0(union(sK19)),sK5(sK19,sK0(union(sK19))))
    | ~ subset(sK5(sK19,sK0(union(sK19))),sK19)
    | element(sK0(union(sK19)),sK19) ),
    inference(instantiation,[status(thm)],[c_13443]) ).

cnf(c_26617,plain,
    ( ~ in(sK0(union(sK19)),sK19)
    | subset(sK0(union(sK19)),union(sK19)) ),
    inference(instantiation,[status(thm)],[c_11749]) ).

cnf(c_27408,plain,
    ( ~ in(sK1(union(sK19)),sK2(union(sK19)))
    | epsilon_connected(union(sK19)) ),
    inference(instantiation,[status(thm)],[c_64]) ).

cnf(c_27656,plain,
    sK2(union(sK19)) = sK2(union(sK19)),
    inference(instantiation,[status(thm)],[c_2609]) ).

cnf(c_46207,plain,
    ( ~ in(sK0(union(sK19)),union(sK19))
    | ~ epsilon_transitive(sK19)
    | subset(sK5(sK19,sK0(union(sK19))),sK19) ),
    inference(instantiation,[status(thm)],[c_4821]) ).

cnf(c_46216,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_46207,c_27656,c_27408,c_26617,c_26272,c_26019,c_21633,c_21257,c_8432,c_8434,c_8413,c_8415,c_7276,c_4481,c_3937,c_3800,c_3719,c_3662,c_3663,c_3664,c_3618,c_3607,c_3608,c_3586,c_3584,c_124,c_81,c_88,c_125]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : NUM397+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.11  % Command  : run_iprover %s %d THM
% 0.10/0.31  % Computer : n013.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Fri Aug 25 09:15:17 EDT 2023
% 0.10/0.32  % CPUTime  : 
% 0.15/0.43  Running first-order theorem proving
% 0.15/0.43  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 39.02/6.20  % SZS status Started for theBenchmark.p
% 39.02/6.20  % SZS status Theorem for theBenchmark.p
% 39.02/6.20  
% 39.02/6.20  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 39.02/6.20  
% 39.02/6.20  ------  iProver source info
% 39.02/6.20  
% 39.02/6.20  git: date: 2023-05-31 18:12:56 +0000
% 39.02/6.20  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 39.02/6.20  git: non_committed_changes: false
% 39.02/6.20  git: last_make_outside_of_git: false
% 39.02/6.20  
% 39.02/6.20  ------ Parsing...
% 39.02/6.20  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 39.02/6.20  
% 39.02/6.20  ------ Preprocessing... sup_sim: 0  sf_s  rm: 22 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 3 0s  sf_e  pe_s  pe_e 
% 39.02/6.20  
% 39.02/6.20  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 39.02/6.20  
% 39.02/6.20  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 39.02/6.20  ------ Proving...
% 39.02/6.20  ------ Problem Properties 
% 39.02/6.20  
% 39.02/6.20  
% 39.02/6.20  clauses                                 58
% 39.02/6.20  conjectures                             2
% 39.02/6.20  EPR                                     40
% 39.02/6.20  Horn                                    49
% 39.02/6.20  unary                                   20
% 39.02/6.20  binary                                  22
% 39.02/6.20  lits                                    121
% 39.02/6.20  lits eq                                 8
% 39.02/6.20  fd_pure                                 0
% 39.02/6.20  fd_pseudo                               0
% 39.02/6.20  fd_cond                                 1
% 39.02/6.20  fd_pseudo_cond                          6
% 39.02/6.20  AC symbols                              0
% 39.02/6.20  
% 39.02/6.20  ------ Input Options Time Limit: Unbounded
% 39.02/6.20  
% 39.02/6.20  
% 39.02/6.20  ------ 
% 39.02/6.20  Current options:
% 39.02/6.20  ------ 
% 39.02/6.20  
% 39.02/6.20  
% 39.02/6.20  
% 39.02/6.20  
% 39.02/6.20  ------ Proving...
% 39.02/6.20  
% 39.02/6.20  
% 39.02/6.20  % SZS status Theorem for theBenchmark.p
% 39.02/6.20  
% 39.02/6.20  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 39.02/6.21  
% 39.02/6.21  
%------------------------------------------------------------------------------