TSTP Solution File: NUM402+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : NUM402+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n008.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 11:30:17 EDT 2023

% Result   : Theorem 110.22s 15.78s
% Output   : CNFRefutation 110.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   15
% Syntax   : Number of formulae    :  113 (   5 unt;   0 def)
%            Number of atoms       :  413 (  29 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  487 ( 187   ~; 196   |;  78   &)
%                                         (   9 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   1 con; 0-2 aty)
%            Number of variables   :  197 (   0 sgn; 133   !;  26   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f8,axiom,
    ! [X0] :
      ( epsilon_transitive(X0)
    <=> ! [X1] :
          ( in(X1,X0)
         => subset(X1,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).

fof(f9,axiom,
    ! [X0] :
      ( epsilon_connected(X0)
    <=> ! [X1,X2] :
          ~ ( ~ in(X2,X1)
            & X1 != X2
            & ~ in(X1,X2)
            & in(X2,X0)
            & in(X1,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_ordinal1) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

fof(f11,axiom,
    ! [X0] :
      ( ordinal(X0)
    <=> ( epsilon_connected(X0)
        & epsilon_transitive(X0) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).

fof(f34,axiom,
    ! [X0,X1] :
      ( ordinal(X1)
     => ( in(X0,X1)
       => ordinal(X0) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',t24_ordinal1) ).

fof(f37,conjecture,
    ! [X0] :
      ( ! [X1] :
          ( in(X1,X0)
         => ordinal(X1) )
     => ordinal(union(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_ordinal1) ).

fof(f38,negated_conjecture,
    ~ ! [X0] :
        ( ! [X1] :
            ( in(X1,X0)
           => ordinal(X1) )
       => ordinal(union(X0)) ),
    inference(negated_conjecture,[],[f37]) ).

fof(f64,plain,
    ! [X0] :
      ( epsilon_transitive(X0)
    <=> ! [X1] :
          ( subset(X1,X0)
          | ~ in(X1,X0) ) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f65,plain,
    ! [X0] :
      ( epsilon_connected(X0)
    <=> ! [X1,X2] :
          ( in(X2,X1)
          | X1 = X2
          | in(X1,X2)
          | ~ in(X2,X0)
          | ~ in(X1,X0) ) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f66,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( ordinal(X0)
      | ~ in(X0,X1)
      | ~ ordinal(X1) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( ordinal(X0)
      | ~ in(X0,X1)
      | ~ ordinal(X1) ),
    inference(flattening,[],[f69]) ).

fof(f71,plain,
    ! [X0] :
      ( ! [X1] :
          ( in(X1,X0)
          | X0 = X1
          | in(X0,X1)
          | ~ ordinal(X1) )
      | ~ ordinal(X0) ),
    inference(ennf_transformation,[],[f35]) ).

fof(f72,plain,
    ! [X0] :
      ( ! [X1] :
          ( in(X1,X0)
          | X0 = X1
          | in(X0,X1)
          | ~ ordinal(X1) )
      | ~ ordinal(X0) ),
    inference(flattening,[],[f71]) ).

fof(f75,plain,
    ? [X0] :
      ( ~ ordinal(union(X0))
      & ! [X1] :
          ( ordinal(X1)
          | ~ in(X1,X0) ) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f82,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,[],[f64]) ).

fof(f83,plain,
    ! [X0] :
      ( ( epsilon_transitive(X0)
        | ? [X1] :
            ( ~ subset(X1,X0)
            & in(X1,X0) ) )
      & ( ! [X2] :
            ( subset(X2,X0)
            | ~ in(X2,X0) )
        | ~ epsilon_transitive(X0) ) ),
    inference(rectify,[],[f82]) ).

fof(f84,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ subset(X1,X0)
          & in(X1,X0) )
     => ( ~ subset(sK0(X0),X0)
        & in(sK0(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f85,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])],[f83,f84]) ).

fof(f86,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,[],[f65]) ).

fof(f87,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,[],[f86]) ).

fof(f88,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(f89,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])],[f87,f88]) ).

fof(f90,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,[],[f66]) ).

fof(f91,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,[],[f90]) ).

fof(f92,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK3(X0,X1),X1)
        & in(sK3(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f93,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK3(X0,X1),X1)
          & in(sK3(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f91,f92]) ).

fof(f94,plain,
    ! [X0] :
      ( ( ordinal(X0)
        | ~ epsilon_connected(X0)
        | ~ epsilon_transitive(X0) )
      & ( ( epsilon_connected(X0)
          & epsilon_transitive(X0) )
        | ~ ordinal(X0) ) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f95,plain,
    ! [X0] :
      ( ( ordinal(X0)
        | ~ epsilon_connected(X0)
        | ~ epsilon_transitive(X0) )
      & ( ( epsilon_connected(X0)
          & epsilon_transitive(X0) )
        | ~ ordinal(X0) ) ),
    inference(flattening,[],[f94]) ).

fof(f96,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(f97,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,[],[f96]) ).

fof(f98,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(sK4(X0,X1),X3) )
          | ~ in(sK4(X0,X1),X1) )
        & ( ? [X4] :
              ( in(X4,X0)
              & in(sK4(X0,X1),X4) )
          | in(sK4(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f99,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( in(X4,X0)
          & in(sK4(X0,X1),X4) )
     => ( in(sK5(X0,X1),X0)
        & in(sK4(X0,X1),sK5(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f100,plain,
    ! [X0,X5] :
      ( ? [X7] :
          ( in(X7,X0)
          & in(X5,X7) )
     => ( in(sK6(X0,X5),X0)
        & in(X5,sK6(X0,X5)) ) ),
    introduced(choice_axiom,[]) ).

fof(f101,plain,
    ! [X0,X1] :
      ( ( union(X0) = X1
        | ( ( ! [X3] :
                ( ~ in(X3,X0)
                | ~ in(sK4(X0,X1),X3) )
            | ~ in(sK4(X0,X1),X1) )
          & ( ( in(sK5(X0,X1),X0)
              & in(sK4(X0,X1),sK5(X0,X1)) )
            | in(sK4(X0,X1),X1) ) ) )
      & ( ! [X5] :
            ( ( in(X5,X1)
              | ! [X6] :
                  ( ~ in(X6,X0)
                  | ~ in(X5,X6) ) )
            & ( ( in(sK6(X0,X5),X0)
                & in(X5,sK6(X0,X5)) )
              | ~ in(X5,X1) ) )
        | union(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f97,f100,f99,f98]) ).

fof(f130,plain,
    ( ? [X0] :
        ( ~ ordinal(union(X0))
        & ! [X1] :
            ( ordinal(X1)
            | ~ in(X1,X0) ) )
   => ( ~ ordinal(union(sK21))
      & ! [X1] :
          ( ordinal(X1)
          | ~ in(X1,sK21) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f131,plain,
    ( ~ ordinal(union(sK21))
    & ! [X1] :
        ( ordinal(X1)
        | ~ in(X1,sK21) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f75,f130]) ).

fof(f144,plain,
    ! [X2,X0] :
      ( subset(X2,X0)
      | ~ in(X2,X0)
      | ~ epsilon_transitive(X0) ),
    inference(cnf_transformation,[],[f85]) ).

fof(f145,plain,
    ! [X0] :
      ( epsilon_transitive(X0)
      | in(sK0(X0),X0) ),
    inference(cnf_transformation,[],[f85]) ).

fof(f146,plain,
    ! [X0] :
      ( epsilon_transitive(X0)
      | ~ subset(sK0(X0),X0) ),
    inference(cnf_transformation,[],[f85]) ).

fof(f148,plain,
    ! [X0] :
      ( epsilon_connected(X0)
      | in(sK1(X0),X0) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f149,plain,
    ! [X0] :
      ( epsilon_connected(X0)
      | in(sK2(X0),X0) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f150,plain,
    ! [X0] :
      ( epsilon_connected(X0)
      | ~ in(sK1(X0),sK2(X0)) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f151,plain,
    ! [X0] :
      ( epsilon_connected(X0)
      | sK1(X0) != sK2(X0) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f152,plain,
    ! [X0] :
      ( epsilon_connected(X0)
      | ~ in(sK2(X0),sK1(X0)) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f153,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | ~ in(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f93]) ).

fof(f154,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sK3(X0,X1),X0) ),
    inference(cnf_transformation,[],[f93]) ).

fof(f155,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ in(sK3(X0,X1),X1) ),
    inference(cnf_transformation,[],[f93]) ).

fof(f156,plain,
    ! [X0] :
      ( epsilon_transitive(X0)
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f95]) ).

fof(f158,plain,
    ! [X0] :
      ( ordinal(X0)
      | ~ epsilon_connected(X0)
      | ~ epsilon_transitive(X0) ),
    inference(cnf_transformation,[],[f95]) ).

fof(f159,plain,
    ! [X0,X1,X5] :
      ( in(X5,sK6(X0,X5))
      | ~ in(X5,X1)
      | union(X0) != X1 ),
    inference(cnf_transformation,[],[f101]) ).

fof(f160,plain,
    ! [X0,X1,X5] :
      ( in(sK6(X0,X5),X0)
      | ~ in(X5,X1)
      | union(X0) != X1 ),
    inference(cnf_transformation,[],[f101]) ).

fof(f161,plain,
    ! [X0,X1,X6,X5] :
      ( in(X5,X1)
      | ~ in(X6,X0)
      | ~ in(X5,X6)
      | union(X0) != X1 ),
    inference(cnf_transformation,[],[f101]) ).

fof(f213,plain,
    ! [X0,X1] :
      ( ordinal(X0)
      | ~ in(X0,X1)
      | ~ ordinal(X1) ),
    inference(cnf_transformation,[],[f70]) ).

fof(f214,plain,
    ! [X0,X1] :
      ( in(X1,X0)
      | X0 = X1
      | in(X0,X1)
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f216,plain,
    ! [X1] :
      ( ordinal(X1)
      | ~ in(X1,sK21) ),
    inference(cnf_transformation,[],[f131]) ).

fof(f217,plain,
    ~ ordinal(union(sK21)),
    inference(cnf_transformation,[],[f131]) ).

fof(f225,plain,
    ! [X0,X6,X5] :
      ( in(X5,union(X0))
      | ~ in(X6,X0)
      | ~ in(X5,X6) ),
    inference(equality_resolution,[],[f161]) ).

fof(f226,plain,
    ! [X0,X5] :
      ( in(sK6(X0,X5),X0)
      | ~ in(X5,union(X0)) ),
    inference(equality_resolution,[],[f160]) ).

fof(f227,plain,
    ! [X0,X5] :
      ( in(X5,sK6(X0,X5))
      | ~ in(X5,union(X0)) ),
    inference(equality_resolution,[],[f159]) ).

cnf(c_58,plain,
    ( ~ subset(sK0(X0),X0)
    | epsilon_transitive(X0) ),
    inference(cnf_transformation,[],[f146]) ).

cnf(c_59,plain,
    ( in(sK0(X0),X0)
    | epsilon_transitive(X0) ),
    inference(cnf_transformation,[],[f145]) ).

cnf(c_60,plain,
    ( ~ in(X0,X1)
    | ~ epsilon_transitive(X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f144]) ).

cnf(c_61,plain,
    ( ~ in(sK2(X0),sK1(X0))
    | epsilon_connected(X0) ),
    inference(cnf_transformation,[],[f152]) ).

cnf(c_62,plain,
    ( sK2(X0) != sK1(X0)
    | epsilon_connected(X0) ),
    inference(cnf_transformation,[],[f151]) ).

cnf(c_63,plain,
    ( ~ in(sK1(X0),sK2(X0))
    | epsilon_connected(X0) ),
    inference(cnf_transformation,[],[f150]) ).

cnf(c_64,plain,
    ( in(sK2(X0),X0)
    | epsilon_connected(X0) ),
    inference(cnf_transformation,[],[f149]) ).

cnf(c_65,plain,
    ( in(sK1(X0),X0)
    | epsilon_connected(X0) ),
    inference(cnf_transformation,[],[f148]) ).

cnf(c_67,plain,
    ( ~ in(sK3(X0,X1),X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f155]) ).

cnf(c_68,plain,
    ( in(sK3(X0,X1),X0)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f154]) ).

cnf(c_69,plain,
    ( ~ in(X0,X1)
    | ~ subset(X1,X2)
    | in(X0,X2) ),
    inference(cnf_transformation,[],[f153]) ).

cnf(c_70,plain,
    ( ~ epsilon_connected(X0)
    | ~ epsilon_transitive(X0)
    | ordinal(X0) ),
    inference(cnf_transformation,[],[f158]) ).

cnf(c_72,plain,
    ( ~ ordinal(X0)
    | epsilon_transitive(X0) ),
    inference(cnf_transformation,[],[f156]) ).

cnf(c_76,plain,
    ( ~ in(X0,X1)
    | ~ in(X1,X2)
    | in(X0,union(X2)) ),
    inference(cnf_transformation,[],[f225]) ).

cnf(c_77,plain,
    ( ~ in(X0,union(X1))
    | in(sK6(X1,X0),X1) ),
    inference(cnf_transformation,[],[f226]) ).

cnf(c_78,plain,
    ( ~ in(X0,union(X1))
    | in(X0,sK6(X1,X0)) ),
    inference(cnf_transformation,[],[f227]) ).

cnf(c_127,plain,
    ( ~ in(X0,X1)
    | ~ ordinal(X1)
    | ordinal(X0) ),
    inference(cnf_transformation,[],[f213]) ).

cnf(c_128,plain,
    ( ~ ordinal(X0)
    | ~ ordinal(X1)
    | X0 = X1
    | in(X0,X1)
    | in(X1,X0) ),
    inference(cnf_transformation,[],[f214]) ).

cnf(c_130,negated_conjecture,
    ~ ordinal(union(sK21)),
    inference(cnf_transformation,[],[f217]) ).

cnf(c_131,negated_conjecture,
    ( ~ in(X0,sK21)
    | ordinal(X0) ),
    inference(cnf_transformation,[],[f216]) ).

cnf(c_3320,plain,
    ( ~ epsilon_connected(union(sK21))
    | ~ epsilon_transitive(union(sK21))
    | ordinal(union(sK21)) ),
    inference(instantiation,[status(thm)],[c_70]) ).

cnf(c_3348,plain,
    ( ~ subset(sK0(union(sK21)),union(sK21))
    | epsilon_transitive(union(sK21)) ),
    inference(instantiation,[status(thm)],[c_58]) ).

cnf(c_3349,plain,
    ( in(sK0(union(sK21)),union(sK21))
    | epsilon_transitive(union(sK21)) ),
    inference(instantiation,[status(thm)],[c_59]) ).

cnf(c_3447,plain,
    ( sK2(union(sK21)) != sK1(union(sK21))
    | epsilon_connected(union(sK21)) ),
    inference(instantiation,[status(thm)],[c_62]) ).

cnf(c_3448,plain,
    ( in(sK1(union(sK21)),union(sK21))
    | epsilon_connected(union(sK21)) ),
    inference(instantiation,[status(thm)],[c_65]) ).

cnf(c_3449,plain,
    ( in(sK2(union(sK21)),union(sK21))
    | epsilon_connected(union(sK21)) ),
    inference(instantiation,[status(thm)],[c_64]) ).

cnf(c_3450,plain,
    ( ~ in(sK1(union(sK21)),sK2(union(sK21)))
    | epsilon_connected(union(sK21)) ),
    inference(instantiation,[status(thm)],[c_63]) ).

cnf(c_3451,plain,
    ( ~ in(sK2(union(sK21)),sK1(union(sK21)))
    | epsilon_connected(union(sK21)) ),
    inference(instantiation,[status(thm)],[c_61]) ).

cnf(c_3469,plain,
    ( ~ in(sK0(union(sK21)),union(sK21))
    | in(sK6(sK21,sK0(union(sK21))),sK21) ),
    inference(instantiation,[status(thm)],[c_77]) ).

cnf(c_3902,plain,
    ( ~ in(sK3(sK0(union(sK21)),union(sK21)),union(sK21))
    | subset(sK0(union(sK21)),union(sK21)) ),
    inference(instantiation,[status(thm)],[c_67]) ).

cnf(c_3971,plain,
    ( ~ in(sK1(union(sK21)),union(sK21))
    | in(sK1(union(sK21)),sK6(sK21,sK1(union(sK21)))) ),
    inference(instantiation,[status(thm)],[c_78]) ).

cnf(c_3980,plain,
    ( ~ ordinal(sK2(union(sK21)))
    | ~ ordinal(sK1(union(sK21)))
    | sK2(union(sK21)) = sK1(union(sK21))
    | in(sK2(union(sK21)),sK1(union(sK21)))
    | in(sK1(union(sK21)),sK2(union(sK21))) ),
    inference(instantiation,[status(thm)],[c_128]) ).

cnf(c_3999,plain,
    ( ~ in(sK2(union(sK21)),union(sK21))
    | in(sK2(union(sK21)),sK6(sK21,sK2(union(sK21)))) ),
    inference(instantiation,[status(thm)],[c_78]) ).

cnf(c_4434,plain,
    ( ~ in(X0,union(sK21))
    | ordinal(sK6(sK21,X0)) ),
    inference(superposition,[status(thm)],[c_77,c_131]) ).

cnf(c_4468,plain,
    ( ~ in(X0,union(X1))
    | ~ epsilon_transitive(sK6(X1,X0))
    | subset(X0,sK6(X1,X0)) ),
    inference(superposition,[status(thm)],[c_78,c_60]) ).

cnf(c_5278,plain,
    ( ordinal(sK6(sK21,sK0(union(sK21))))
    | epsilon_transitive(union(sK21)) ),
    inference(superposition,[status(thm)],[c_59,c_4434]) ).

cnf(c_5280,plain,
    ( ordinal(sK6(sK21,sK2(union(sK21))))
    | epsilon_connected(union(sK21)) ),
    inference(superposition,[status(thm)],[c_64,c_4434]) ).

cnf(c_5282,plain,
    ( ordinal(sK6(sK21,sK1(union(sK21))))
    | epsilon_connected(union(sK21)) ),
    inference(superposition,[status(thm)],[c_65,c_4434]) ).

cnf(c_5302,plain,
    ( epsilon_transitive(sK6(sK21,sK0(union(sK21))))
    | epsilon_transitive(union(sK21)) ),
    inference(superposition,[status(thm)],[c_5278,c_72]) ).

cnf(c_5304,plain,
    ( epsilon_transitive(sK6(sK21,sK2(union(sK21))))
    | epsilon_connected(union(sK21)) ),
    inference(superposition,[status(thm)],[c_5280,c_72]) ).

cnf(c_5510,plain,
    ( ~ in(sK1(union(sK21)),sK6(sK21,sK1(union(sK21))))
    | ~ ordinal(sK6(sK21,sK1(union(sK21))))
    | ordinal(sK1(union(sK21))) ),
    inference(instantiation,[status(thm)],[c_127]) ).

cnf(c_5578,plain,
    ( ~ in(sK2(union(sK21)),sK6(sK21,sK2(union(sK21))))
    | ~ ordinal(sK6(sK21,sK2(union(sK21))))
    | ordinal(sK2(union(sK21))) ),
    inference(instantiation,[status(thm)],[c_127]) ).

cnf(c_5678,plain,
    ( ~ subset(X0,X1)
    | in(sK3(X0,X2),X1)
    | subset(X0,X2) ),
    inference(superposition,[status(thm)],[c_68,c_69]) ).

cnf(c_7712,plain,
    epsilon_transitive(sK6(sK21,sK0(union(sK21)))),
    inference(global_subsumption_just,[status(thm)],[c_5302,c_130,c_3320,c_3451,c_3450,c_3449,c_3448,c_3447,c_3971,c_3980,c_3999,c_5280,c_5282,c_5302,c_5510,c_5578]) ).

cnf(c_7714,plain,
    epsilon_connected(union(sK21)),
    inference(global_subsumption_just,[status(thm)],[c_5304,c_3451,c_3450,c_3449,c_3448,c_3447,c_3971,c_3980,c_3999,c_5280,c_5282,c_5510,c_5578]) ).

cnf(c_37015,plain,
    ( ~ subset(sK0(union(sK21)),X0)
    | in(sK3(sK0(union(sK21)),union(sK21)),X0)
    | subset(sK0(union(sK21)),union(sK21)) ),
    inference(instantiation,[status(thm)],[c_5678]) ).

cnf(c_37029,plain,
    ( ~ in(sK0(union(sK21)),union(sK21))
    | ~ epsilon_transitive(sK6(sK21,sK0(union(sK21))))
    | subset(sK0(union(sK21)),sK6(sK21,sK0(union(sK21)))) ),
    inference(instantiation,[status(thm)],[c_4468]) ).

cnf(c_41288,plain,
    ( ~ subset(sK0(union(sK21)),sK6(sK21,sK0(union(sK21))))
    | in(sK3(sK0(union(sK21)),union(sK21)),sK6(sK21,sK0(union(sK21))))
    | subset(sK0(union(sK21)),union(sK21)) ),
    inference(instantiation,[status(thm)],[c_37015]) ).

cnf(c_127010,plain,
    ( ~ in(X0,sK6(sK21,sK0(union(sK21))))
    | ~ in(sK6(sK21,sK0(union(sK21))),sK21)
    | in(X0,union(sK21)) ),
    inference(instantiation,[status(thm)],[c_76]) ).

cnf(c_156034,plain,
    ( ~ in(sK3(sK0(union(sK21)),union(sK21)),sK6(sK21,sK0(union(sK21))))
    | ~ in(sK6(sK21,sK0(union(sK21))),sK21)
    | in(sK3(sK0(union(sK21)),union(sK21)),union(sK21)) ),
    inference(instantiation,[status(thm)],[c_127010]) ).

cnf(c_156035,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_156034,c_41288,c_37029,c_7714,c_7712,c_3902,c_3469,c_3348,c_3349,c_3320,c_130]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15  % Problem  : NUM402+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.15  % Command  : run_iprover %s %d THM
% 0.13/0.36  % Computer : n008.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit : 300
% 0.13/0.36  % WCLimit  : 300
% 0.13/0.36  % DateTime : Fri Aug 25 18:05:03 EDT 2023
% 0.13/0.36  % CPUTime  : 
% 0.19/0.48  Running first-order theorem proving
% 0.19/0.48  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 110.22/15.78  % SZS status Started for theBenchmark.p
% 110.22/15.78  % SZS status Theorem for theBenchmark.p
% 110.22/15.78  
% 110.22/15.78  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 110.22/15.78  
% 110.22/15.78  ------  iProver source info
% 110.22/15.78  
% 110.22/15.78  git: date: 2023-05-31 18:12:56 +0000
% 110.22/15.78  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 110.22/15.78  git: non_committed_changes: false
% 110.22/15.78  git: last_make_outside_of_git: false
% 110.22/15.78  
% 110.22/15.78  ------ Parsing...
% 110.22/15.78  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 110.22/15.78  
% 110.22/15.78  ------ 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 
% 110.22/15.78  
% 110.22/15.78  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 110.22/15.78  
% 110.22/15.78  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 110.22/15.78  ------ Proving...
% 110.22/15.78  ------ Problem Properties 
% 110.22/15.78  
% 110.22/15.78  
% 110.22/15.78  clauses                                 61
% 110.22/15.78  conjectures                             2
% 110.22/15.78  EPR                                     39
% 110.22/15.78  Horn                                    52
% 110.22/15.78  unary                                   23
% 110.22/15.78  binary                                  24
% 110.22/15.78  lits                                    119
% 110.22/15.78  lits eq                                 8
% 110.22/15.78  fd_pure                                 0
% 110.22/15.78  fd_pseudo                               0
% 110.22/15.78  fd_cond                                 1
% 110.22/15.78  fd_pseudo_cond                          6
% 110.22/15.78  AC symbols                              0
% 110.22/15.78  
% 110.22/15.78  ------ Input Options Time Limit: Unbounded
% 110.22/15.78  
% 110.22/15.78  
% 110.22/15.78  ------ 
% 110.22/15.78  Current options:
% 110.22/15.78  ------ 
% 110.22/15.78  
% 110.22/15.78  
% 110.22/15.78  
% 110.22/15.78  
% 110.22/15.78  ------ Proving...
% 110.22/15.78  
% 110.22/15.78  
% 110.22/15.78  % SZS status Theorem for theBenchmark.p
% 110.22/15.78  
% 110.22/15.78  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 110.22/15.78  
% 110.22/15.79  
%------------------------------------------------------------------------------