TSTP Solution File: SEU236+3 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SEU236+3 : 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 17:05:03 EDT 2023

% Result   : Theorem 7.20s 1.66s
% Output   : CNFRefutation 7.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   19
% Syntax   : Number of formulae    :  109 (  20 unt;   0 def)
%            Number of atoms       :  350 (  32 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  391 ( 150   ~; 152   |;  60   &)
%                                         (  11 <=>;  17  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   2 con; 0-2 aty)
%            Number of variables   :  173 (   1 sgn; 114   !;  21   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [X0] :
      ( ordinal(X0)
     => ( epsilon_connected(X0)
        & epsilon_transitive(X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).

fof(f10,axiom,
    ! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).

fof(f11,axiom,
    ! [X0,X1] :
      ( singleton(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).

fof(f12,axiom,
    ! [X0] :
      ( epsilon_transitive(X0)
    <=> ! [X1] :
          ( in(X1,X0)
         => subset(X1,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).

fof(f13,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

fof(f14,axiom,
    ! [X0] :
    ? [X1] : element(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).

fof(f21,axiom,
    ! [X0] :
      ( ordinal(X0)
     => ( ordinal(succ(X0))
        & epsilon_connected(succ(X0))
        & epsilon_transitive(succ(X0))
        & ~ empty(succ(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_ordinal1) ).

fof(f38,axiom,
    ! [X0,X1] :
      ( ( ordinal(X1)
        & ordinal(X0) )
     => ( ordinal_subset(X0,X1)
      <=> subset(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).

fof(f41,axiom,
    ! [X0] : in(X0,succ(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_ordinal1) ).

fof(f44,axiom,
    ! [X0,X1] :
      ( element(X0,X1)
     => ( in(X0,X1)
        | empty(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).

fof(f45,conjecture,
    ! [X0] :
      ( ordinal(X0)
     => ! [X1] :
          ( ordinal(X1)
         => ( in(X0,X1)
          <=> ordinal_subset(succ(X0),X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_ordinal1) ).

fof(f46,negated_conjecture,
    ~ ! [X0] :
        ( ordinal(X0)
       => ! [X1] :
            ( ordinal(X1)
           => ( in(X0,X1)
            <=> ordinal_subset(succ(X0),X1) ) ) ),
    inference(negated_conjecture,[],[f45]) ).

fof(f51,axiom,
    ! [X0,X1] :
      ~ ( empty(X1)
        & in(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).

fof(f53,axiom,
    ! [X0,X1,X2] :
      ( ( subset(X2,X1)
        & subset(X0,X1) )
     => subset(set_union2(X0,X2),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).

fof(f67,plain,
    ! [X0] :
      ( ( epsilon_connected(X0)
        & epsilon_transitive(X0) )
      | ~ ordinal(X0) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f76,plain,
    ! [X0] :
      ( epsilon_transitive(X0)
    <=> ! [X1] :
          ( subset(X1,X0)
          | ~ in(X1,X0) ) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f81,plain,
    ! [X0] :
      ( ( ordinal(succ(X0))
        & epsilon_connected(succ(X0))
        & epsilon_transitive(succ(X0))
        & ~ empty(succ(X0)) )
      | ~ ordinal(X0) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( ( ordinal_subset(X0,X1)
      <=> subset(X0,X1) )
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f84,plain,
    ! [X0,X1] :
      ( ( ordinal_subset(X0,X1)
      <=> subset(X0,X1) )
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(flattening,[],[f83]) ).

fof(f88,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(ennf_transformation,[],[f44]) ).

fof(f89,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(flattening,[],[f88]) ).

fof(f90,plain,
    ? [X0] :
      ( ? [X1] :
          ( ( in(X0,X1)
          <~> ordinal_subset(succ(X0),X1) )
          & ordinal(X1) )
      & ordinal(X0) ),
    inference(ennf_transformation,[],[f46]) ).

fof(f95,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f51]) ).

fof(f97,plain,
    ! [X0,X1,X2] :
      ( subset(set_union2(X0,X2),X1)
      | ~ subset(X2,X1)
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f53]) ).

fof(f98,plain,
    ! [X0,X1,X2] :
      ( subset(set_union2(X0,X2),X1)
      | ~ subset(X2,X1)
      | ~ subset(X0,X1) ),
    inference(flattening,[],[f97]) ).

fof(f99,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,[],[f11]) ).

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

fof(f101,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( X0 != X2
            | ~ in(X2,X1) )
          & ( X0 = X2
            | in(X2,X1) ) )
     => ( ( sK0(X0,X1) != X0
          | ~ in(sK0(X0,X1),X1) )
        & ( sK0(X0,X1) = X0
          | in(sK0(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f102,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ( ( sK0(X0,X1) != X0
            | ~ in(sK0(X0,X1),X1) )
          & ( sK0(X0,X1) = X0
            | in(sK0(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f100,f101]) ).

fof(f103,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,[],[f76]) ).

fof(f104,plain,
    ! [X0] :
      ( ( epsilon_transitive(X0)
        | ? [X1] :
            ( ~ subset(X1,X0)
            & in(X1,X0) ) )
      & ( ! [X2] :
            ( subset(X2,X0)
            | ~ in(X2,X0) )
        | ~ epsilon_transitive(X0) ) ),
    inference(rectify,[],[f103]) ).

fof(f105,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ subset(X1,X0)
          & in(X1,X0) )
     => ( ~ subset(sK1(X0),X0)
        & in(sK1(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f106,plain,
    ! [X0] :
      ( ( epsilon_transitive(X0)
        | ( ~ subset(sK1(X0),X0)
          & in(sK1(X0),X0) ) )
      & ( ! [X2] :
            ( subset(X2,X0)
            | ~ in(X2,X0) )
        | ~ epsilon_transitive(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f104,f105]) ).

fof(f107,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,[],[f77]) ).

fof(f108,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,[],[f107]) ).

fof(f109,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK2(X0,X1),X1)
        & in(sK2(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f110,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK2(X0,X1),X1)
          & in(sK2(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f108,f109]) ).

fof(f111,plain,
    ! [X0] :
      ( ? [X1] : element(X1,X0)
     => element(sK3(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f112,plain,
    ! [X0] : element(sK3(X0),X0),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f14,f111]) ).

fof(f139,plain,
    ! [X0,X1] :
      ( ( ( ordinal_subset(X0,X1)
          | ~ subset(X0,X1) )
        & ( subset(X0,X1)
          | ~ ordinal_subset(X0,X1) ) )
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(nnf_transformation,[],[f84]) ).

fof(f140,plain,
    ? [X0] :
      ( ? [X1] :
          ( ( ~ ordinal_subset(succ(X0),X1)
            | ~ in(X0,X1) )
          & ( ordinal_subset(succ(X0),X1)
            | in(X0,X1) )
          & ordinal(X1) )
      & ordinal(X0) ),
    inference(nnf_transformation,[],[f90]) ).

fof(f141,plain,
    ? [X0] :
      ( ? [X1] :
          ( ( ~ ordinal_subset(succ(X0),X1)
            | ~ in(X0,X1) )
          & ( ordinal_subset(succ(X0),X1)
            | in(X0,X1) )
          & ordinal(X1) )
      & ordinal(X0) ),
    inference(flattening,[],[f140]) ).

fof(f142,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ( ~ ordinal_subset(succ(X0),X1)
              | ~ in(X0,X1) )
            & ( ordinal_subset(succ(X0),X1)
              | in(X0,X1) )
            & ordinal(X1) )
        & ordinal(X0) )
   => ( ? [X1] :
          ( ( ~ ordinal_subset(succ(sK17),X1)
            | ~ in(sK17,X1) )
          & ( ordinal_subset(succ(sK17),X1)
            | in(sK17,X1) )
          & ordinal(X1) )
      & ordinal(sK17) ) ),
    introduced(choice_axiom,[]) ).

fof(f143,plain,
    ( ? [X1] :
        ( ( ~ ordinal_subset(succ(sK17),X1)
          | ~ in(sK17,X1) )
        & ( ordinal_subset(succ(sK17),X1)
          | in(sK17,X1) )
        & ordinal(X1) )
   => ( ( ~ ordinal_subset(succ(sK17),sK18)
        | ~ in(sK17,sK18) )
      & ( ordinal_subset(succ(sK17),sK18)
        | in(sK17,sK18) )
      & ordinal(sK18) ) ),
    introduced(choice_axiom,[]) ).

fof(f144,plain,
    ( ( ~ ordinal_subset(succ(sK17),sK18)
      | ~ in(sK17,sK18) )
    & ( ordinal_subset(succ(sK17),sK18)
      | in(sK17,sK18) )
    & ordinal(sK18)
    & ordinal(sK17) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18])],[f141,f143,f142]) ).

fof(f148,plain,
    ! [X0] :
      ( epsilon_transitive(X0)
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f159,plain,
    ! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
    inference(cnf_transformation,[],[f10]) ).

fof(f160,plain,
    ! [X3,X0,X1] :
      ( X0 = X3
      | ~ in(X3,X1)
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f102]) ).

fof(f164,plain,
    ! [X2,X0] :
      ( subset(X2,X0)
      | ~ in(X2,X0)
      | ~ epsilon_transitive(X0) ),
    inference(cnf_transformation,[],[f106]) ).

fof(f167,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | ~ in(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f110]) ).

fof(f168,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sK2(X0,X1),X0) ),
    inference(cnf_transformation,[],[f110]) ).

fof(f169,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ in(sK2(X0,X1),X1) ),
    inference(cnf_transformation,[],[f110]) ).

fof(f170,plain,
    ! [X0] : element(sK3(X0),X0),
    inference(cnf_transformation,[],[f112]) ).

fof(f186,plain,
    ! [X0] :
      ( ordinal(succ(X0))
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f81]) ).

fof(f222,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ ordinal_subset(X0,X1)
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f139]) ).

fof(f223,plain,
    ! [X0,X1] :
      ( ordinal_subset(X0,X1)
      | ~ subset(X0,X1)
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f139]) ).

fof(f226,plain,
    ! [X0] : in(X0,succ(X0)),
    inference(cnf_transformation,[],[f41]) ).

fof(f229,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f230,plain,
    ordinal(sK17),
    inference(cnf_transformation,[],[f144]) ).

fof(f231,plain,
    ordinal(sK18),
    inference(cnf_transformation,[],[f144]) ).

fof(f232,plain,
    ( ordinal_subset(succ(sK17),sK18)
    | in(sK17,sK18) ),
    inference(cnf_transformation,[],[f144]) ).

fof(f233,plain,
    ( ~ ordinal_subset(succ(sK17),sK18)
    | ~ in(sK17,sK18) ),
    inference(cnf_transformation,[],[f144]) ).

fof(f239,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f95]) ).

fof(f241,plain,
    ! [X2,X0,X1] :
      ( subset(set_union2(X0,X2),X1)
      | ~ subset(X2,X1)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f98]) ).

fof(f243,plain,
    ! [X0] :
      ( ordinal(set_union2(X0,singleton(X0)))
      | ~ ordinal(X0) ),
    inference(definition_unfolding,[],[f186,f159]) ).

fof(f247,plain,
    ! [X0] : in(X0,set_union2(X0,singleton(X0))),
    inference(definition_unfolding,[],[f226,f159]) ).

fof(f248,plain,
    ( ~ ordinal_subset(set_union2(sK17,singleton(sK17)),sK18)
    | ~ in(sK17,sK18) ),
    inference(definition_unfolding,[],[f233,f159]) ).

fof(f249,plain,
    ( ordinal_subset(set_union2(sK17,singleton(sK17)),sK18)
    | in(sK17,sK18) ),
    inference(definition_unfolding,[],[f232,f159]) ).

fof(f252,plain,
    ! [X3,X0] :
      ( X0 = X3
      | ~ in(X3,singleton(X0)) ),
    inference(equality_resolution,[],[f160]) ).

cnf(c_52,plain,
    ( ~ ordinal(X0)
    | epsilon_transitive(X0) ),
    inference(cnf_transformation,[],[f148]) ).

cnf(c_63,plain,
    ( ~ in(X0,singleton(X1))
    | X0 = X1 ),
    inference(cnf_transformation,[],[f252]) ).

cnf(c_66,plain,
    ( ~ in(X0,X1)
    | ~ epsilon_transitive(X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f164]) ).

cnf(c_67,plain,
    ( ~ in(sK2(X0,X1),X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f169]) ).

cnf(c_68,plain,
    ( in(sK2(X0,X1),X0)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f168]) ).

cnf(c_69,plain,
    ( ~ in(X0,X1)
    | ~ subset(X1,X2)
    | in(X0,X2) ),
    inference(cnf_transformation,[],[f167]) ).

cnf(c_70,plain,
    element(sK3(X0),X0),
    inference(cnf_transformation,[],[f170]) ).

cnf(c_83,plain,
    ( ~ ordinal(X0)
    | ordinal(set_union2(X0,singleton(X0))) ),
    inference(cnf_transformation,[],[f243]) ).

cnf(c_122,plain,
    ( ~ subset(X0,X1)
    | ~ ordinal(X0)
    | ~ ordinal(X1)
    | ordinal_subset(X0,X1) ),
    inference(cnf_transformation,[],[f223]) ).

cnf(c_123,plain,
    ( ~ ordinal_subset(X0,X1)
    | ~ ordinal(X0)
    | ~ ordinal(X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f222]) ).

cnf(c_126,plain,
    in(X0,set_union2(X0,singleton(X0))),
    inference(cnf_transformation,[],[f247]) ).

cnf(c_129,plain,
    ( ~ element(X0,X1)
    | in(X0,X1)
    | empty(X1) ),
    inference(cnf_transformation,[],[f229]) ).

cnf(c_130,negated_conjecture,
    ( ~ ordinal_subset(set_union2(sK17,singleton(sK17)),sK18)
    | ~ in(sK17,sK18) ),
    inference(cnf_transformation,[],[f248]) ).

cnf(c_131,negated_conjecture,
    ( ordinal_subset(set_union2(sK17,singleton(sK17)),sK18)
    | in(sK17,sK18) ),
    inference(cnf_transformation,[],[f249]) ).

cnf(c_132,negated_conjecture,
    ordinal(sK18),
    inference(cnf_transformation,[],[f231]) ).

cnf(c_133,negated_conjecture,
    ordinal(sK17),
    inference(cnf_transformation,[],[f230]) ).

cnf(c_139,plain,
    ( ~ in(X0,X1)
    | ~ empty(X1) ),
    inference(cnf_transformation,[],[f239]) ).

cnf(c_141,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X2,X1)
    | subset(set_union2(X0,X2),X1) ),
    inference(cnf_transformation,[],[f241]) ).

cnf(c_2607,plain,
    epsilon_transitive(sK18),
    inference(superposition,[status(thm)],[c_132,c_52]) ).

cnf(c_3410,plain,
    ( in(sK3(X0),X0)
    | empty(X0) ),
    inference(superposition,[status(thm)],[c_70,c_129]) ).

cnf(c_3445,plain,
    ( ~ subset(set_union2(X0,singleton(X0)),X1)
    | in(X0,X1) ),
    inference(superposition,[status(thm)],[c_126,c_69]) ).

cnf(c_3447,plain,
    ( ~ subset(X0,X1)
    | in(sK3(X0),X1)
    | empty(X0) ),
    inference(superposition,[status(thm)],[c_3410,c_69]) ).

cnf(c_3571,plain,
    ( ~ ordinal(set_union2(sK17,singleton(sK17)))
    | ~ ordinal(sK18)
    | subset(set_union2(sK17,singleton(sK17)),sK18)
    | in(sK17,sK18) ),
    inference(superposition,[status(thm)],[c_131,c_123]) ).

cnf(c_3721,plain,
    ( ~ ordinal(set_union2(sK17,singleton(sK17)))
    | subset(set_union2(sK17,singleton(sK17)),sK18)
    | in(sK17,sK18) ),
    inference(global_subsumption_just,[status(thm)],[c_3571,c_132,c_3571]) ).

cnf(c_3917,plain,
    ( ~ ordinal(set_union2(sK17,singleton(sK17)))
    | in(sK17,sK18) ),
    inference(superposition,[status(thm)],[c_3721,c_3445]) ).

cnf(c_3952,plain,
    ( ~ subset(X0,X1)
    | ~ empty(X1)
    | empty(X0) ),
    inference(superposition,[status(thm)],[c_3447,c_139]) ).

cnf(c_4052,plain,
    ( ~ ordinal(set_union2(sK17,singleton(sK17)))
    | ~ empty(sK18)
    | empty(set_union2(sK17,singleton(sK17)))
    | in(sK17,sK18) ),
    inference(superposition,[status(thm)],[c_3721,c_3952]) ).

cnf(c_4329,plain,
    ( ~ ordinal(sK17)
    | in(sK17,sK18) ),
    inference(superposition,[status(thm)],[c_83,c_3917]) ).

cnf(c_4330,plain,
    in(sK17,sK18),
    inference(global_subsumption_just,[status(thm)],[c_4052,c_133,c_4329]) ).

cnf(c_4333,plain,
    ( ~ epsilon_transitive(sK18)
    | subset(sK17,sK18) ),
    inference(superposition,[status(thm)],[c_4330,c_66]) ).

cnf(c_6981,plain,
    ( ~ ordinal(sK17)
    | ordinal(set_union2(sK17,singleton(sK17))) ),
    inference(instantiation,[status(thm)],[c_83]) ).

cnf(c_7830,negated_conjecture,
    ~ ordinal_subset(set_union2(sK17,singleton(sK17)),sK18),
    inference(global_subsumption_just,[status(thm)],[c_130,c_133,c_130,c_4329]) ).

cnf(c_7925,plain,
    ( sK2(singleton(X0),X1) = X0
    | subset(singleton(X0),X1) ),
    inference(superposition,[status(thm)],[c_68,c_63]) ).

cnf(c_8034,plain,
    ( ~ ordinal(set_union2(X0,X1))
    | ~ subset(X0,X2)
    | ~ subset(X1,X2)
    | ~ ordinal(X2)
    | ordinal_subset(set_union2(X0,X1),X2) ),
    inference(superposition,[status(thm)],[c_141,c_122]) ).

cnf(c_10999,plain,
    ( ~ ordinal(set_union2(sK17,singleton(sK17)))
    | ~ subset(singleton(sK17),sK18)
    | ~ subset(sK17,sK18)
    | ~ ordinal(sK18) ),
    inference(superposition,[status(thm)],[c_8034,c_7830]) ).

cnf(c_11043,plain,
    ~ subset(singleton(sK17),sK18),
    inference(global_subsumption_just,[status(thm)],[c_10999,c_133,c_132,c_2607,c_4333,c_6981,c_10999]) ).

cnf(c_11046,plain,
    sK2(singleton(sK17),sK18) = sK17,
    inference(superposition,[status(thm)],[c_7925,c_11043]) ).

cnf(c_11051,plain,
    ( ~ in(sK17,sK18)
    | subset(singleton(sK17),sK18) ),
    inference(superposition,[status(thm)],[c_11046,c_67]) ).

cnf(c_11053,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_11051,c_10999,c_6981,c_4333,c_4329,c_2607,c_132,c_133]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU236+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n008.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Wed Aug 23 16:06:18 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.47  Running first-order theorem proving
% 0.20/0.47  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.20/1.66  % SZS status Started for theBenchmark.p
% 7.20/1.66  % SZS status Theorem for theBenchmark.p
% 7.20/1.66  
% 7.20/1.66  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 7.20/1.66  
% 7.20/1.66  ------  iProver source info
% 7.20/1.66  
% 7.20/1.66  git: date: 2023-05-31 18:12:56 +0000
% 7.20/1.66  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 7.20/1.66  git: non_committed_changes: false
% 7.20/1.66  git: last_make_outside_of_git: false
% 7.20/1.66  
% 7.20/1.66  ------ Parsing...
% 7.20/1.66  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 7.20/1.66  
% 7.20/1.66  ------ Preprocessing... sup_sim: 0  sf_s  rm: 23 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 0  sf_s  rm: 4 0s  sf_e  pe_s  pe_e 
% 7.20/1.66  
% 7.20/1.66  ------ Preprocessing... gs_s  sp: 2 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 7.20/1.66  
% 7.20/1.66  ------ Preprocessing... sf_s  rm: 3 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 7.20/1.66  ------ Proving...
% 7.20/1.66  ------ Problem Properties 
% 7.20/1.66  
% 7.20/1.66  
% 7.20/1.66  clauses                                 61
% 7.20/1.66  conjectures                             4
% 7.20/1.66  EPR                                     38
% 7.20/1.66  Horn                                    54
% 7.20/1.66  unary                                   26
% 7.20/1.66  binary                                  22
% 7.20/1.66  lits                                    112
% 7.20/1.66  lits eq                                 10
% 7.20/1.66  fd_pure                                 0
% 7.20/1.66  fd_pseudo                               0
% 7.20/1.66  fd_cond                                 1
% 7.20/1.66  fd_pseudo_cond                          3
% 7.20/1.66  AC symbols                              0
% 7.20/1.66  
% 7.20/1.66  ------ Input Options Time Limit: Unbounded
% 7.20/1.66  
% 7.20/1.66  
% 7.20/1.66  ------ 
% 7.20/1.66  Current options:
% 7.20/1.66  ------ 
% 7.20/1.66  
% 7.20/1.66  
% 7.20/1.66  
% 7.20/1.66  
% 7.20/1.66  ------ Proving...
% 7.20/1.66  
% 7.20/1.66  
% 7.20/1.66  % SZS status Theorem for theBenchmark.p
% 7.20/1.66  
% 7.20/1.66  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.20/1.66  
% 7.20/1.66  
%------------------------------------------------------------------------------