TSTP Solution File: SEU235+3 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SEU235+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n007.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 : Fri May  3 03:05:08 EDT 2024

% Result   : Theorem 4.09s 1.16s
% Output   : CNFRefutation 4.09s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   21
% Syntax   : Number of formulae    :  129 (  20 unt;   0 def)
%            Number of atoms       :  413 (  26 equ)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives :  502 ( 218   ~; 193   |;  63   &)
%                                         (   6 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   3 con; 0-1 aty)
%            Number of variables   :  203 (   6 sgn 127   !;  18   ?)

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

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

fof(f14,axiom,
    ( relation(empty_set)
    & empty(empty_set) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).

fof(f28,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(f30,axiom,
    ! [X0,X1] : subset(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

fof(f32,axiom,
    ! [X0,X1] :
      ( ordinal(X1)
     => ( in(X0,X1)
       => ordinal(X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_ordinal1) ).

fof(f33,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(f34,axiom,
    ! [X0,X1] :
      ( element(X0,X1)
     => ( in(X0,X1)
        | empty(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).

fof(f35,conjecture,
    ! [X0,X1] :
      ( ordinal(X1)
     => ~ ( ! [X2] :
              ( ordinal(X2)
             => ~ ( ! [X3] :
                      ( ordinal(X3)
                     => ( in(X3,X0)
                       => ordinal_subset(X2,X3) ) )
                  & in(X2,X0) ) )
          & empty_set != X0
          & subset(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_ordinal1) ).

fof(f36,negated_conjecture,
    ~ ! [X0,X1] :
        ( ordinal(X1)
       => ~ ( ! [X2] :
                ( ordinal(X2)
               => ~ ( ! [X3] :
                        ( ordinal(X3)
                       => ( in(X3,X0)
                         => ordinal_subset(X2,X3) ) )
                    & in(X2,X0) ) )
            & empty_set != X0
            & subset(X0,X1) ) ),
    inference(negated_conjecture,[],[f35]) ).

fof(f37,axiom,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).

fof(f38,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,X1,X2] :
      ~ ( empty(X2)
        & element(X1,powerset(X2))
        & in(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).

fof(f42,axiom,
    ! [X0,X1] :
      ~ ( ! [X2] :
            ~ ( ! [X3] :
                  ~ ( in(X3,X2)
                    & in(X3,X1) )
              & in(X2,X1) )
        & in(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_tarski) ).

fof(f43,axiom,
    ! [X0,X1] :
      ~ ( empty(X1)
        & X0 != X1
        & empty(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).

fof(f44,plain,
    ! [X0] : subset(X0,X0),
    inference(rectify,[],[f30]) ).

fof(f56,plain,
    ! [X0] :
      ( ( epsilon_connected(X0)
        & epsilon_transitive(X0) )
      | ~ ordinal(X0) ),
    inference(ennf_transformation,[],[f3]) ).

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

fof(f66,plain,
    ! [X0,X1] :
      ( ( ordinal_subset(X0,X1)
      <=> subset(X0,X1) )
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f67,plain,
    ! [X0,X1] :
      ( ( ordinal_subset(X0,X1)
      <=> subset(X0,X1) )
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(flattening,[],[f66]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( ordinal(X0)
      | ~ in(X0,X1)
      | ~ ordinal(X1) ),
    inference(ennf_transformation,[],[f32]) ).

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

fof(f73,plain,
    ! [X0] :
      ( ! [X1] :
          ( in(X1,X0)
          | X0 = X1
          | in(X0,X1)
          | ~ ordinal(X1) )
      | ~ ordinal(X0) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f74,plain,
    ! [X0] :
      ( ! [X1] :
          ( in(X1,X0)
          | X0 = X1
          | in(X0,X1)
          | ~ ordinal(X1) )
      | ~ ordinal(X0) ),
    inference(flattening,[],[f73]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(flattening,[],[f75]) ).

fof(f77,plain,
    ? [X0,X1] :
      ( ! [X2] :
          ( ? [X3] :
              ( ~ ordinal_subset(X2,X3)
              & in(X3,X0)
              & ordinal(X3) )
          | ~ in(X2,X0)
          | ~ ordinal(X2) )
      & empty_set != X0
      & subset(X0,X1)
      & ordinal(X1) ),
    inference(ennf_transformation,[],[f36]) ).

fof(f78,plain,
    ? [X0,X1] :
      ( ! [X2] :
          ( ? [X3] :
              ( ~ ordinal_subset(X2,X3)
              & in(X3,X0)
              & ordinal(X3) )
          | ~ in(X2,X0)
          | ~ ordinal(X2) )
      & empty_set != X0
      & subset(X0,X1)
      & ordinal(X1) ),
    inference(flattening,[],[f77]) ).

fof(f79,plain,
    ! [X0,X1,X2] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f80,plain,
    ! [X0,X1,X2] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(flattening,[],[f79]) ).

fof(f81,plain,
    ! [X0,X1,X2] :
      ( ~ empty(X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f39]) ).

fof(f84,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ! [X3] :
              ( ~ in(X3,X2)
              | ~ in(X3,X1) )
          & in(X2,X1) )
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f42]) ).

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

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

fof(f87,plain,
    ! [X0] :
      ( ( epsilon_transitive(X0)
        | ? [X1] :
            ( ~ subset(X1,X0)
            & in(X1,X0) ) )
      & ( ! [X2] :
            ( subset(X2,X0)
            | ~ in(X2,X0) )
        | ~ epsilon_transitive(X0) ) ),
    inference(rectify,[],[f86]) ).

fof(f88,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ subset(X1,X0)
          & in(X1,X0) )
     => ( ~ subset(sK0(X0),X0)
        & in(sK0(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

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

fof(f90,plain,
    ! [X0] :
      ( ? [X1] : element(X1,X0)
     => element(sK1(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f91,plain,
    ! [X0] : element(sK1(X0),X0),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f10,f90]) ).

fof(f118,plain,
    ! [X0,X1] :
      ( ( ( ordinal_subset(X0,X1)
          | ~ subset(X0,X1) )
        & ( subset(X0,X1)
          | ~ ordinal_subset(X0,X1) ) )
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(nnf_transformation,[],[f67]) ).

fof(f119,plain,
    ( ? [X0,X1] :
        ( ! [X2] :
            ( ? [X3] :
                ( ~ ordinal_subset(X2,X3)
                & in(X3,X0)
                & ordinal(X3) )
            | ~ in(X2,X0)
            | ~ ordinal(X2) )
        & empty_set != X0
        & subset(X0,X1)
        & ordinal(X1) )
   => ( ! [X2] :
          ( ? [X3] :
              ( ~ ordinal_subset(X2,X3)
              & in(X3,sK15)
              & ordinal(X3) )
          | ~ in(X2,sK15)
          | ~ ordinal(X2) )
      & empty_set != sK15
      & subset(sK15,sK16)
      & ordinal(sK16) ) ),
    introduced(choice_axiom,[]) ).

fof(f120,plain,
    ! [X2] :
      ( ? [X3] :
          ( ~ ordinal_subset(X2,X3)
          & in(X3,sK15)
          & ordinal(X3) )
     => ( ~ ordinal_subset(X2,sK17(X2))
        & in(sK17(X2),sK15)
        & ordinal(sK17(X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f121,plain,
    ( ! [X2] :
        ( ( ~ ordinal_subset(X2,sK17(X2))
          & in(sK17(X2),sK15)
          & ordinal(sK17(X2)) )
        | ~ in(X2,sK15)
        | ~ ordinal(X2) )
    & empty_set != sK15
    & subset(sK15,sK16)
    & ordinal(sK16) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16,sK17])],[f78,f120,f119]) ).

fof(f122,plain,
    ! [X0,X1] :
      ( ( element(X0,powerset(X1))
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ~ element(X0,powerset(X1)) ) ),
    inference(nnf_transformation,[],[f37]) ).

fof(f123,plain,
    ! [X1] :
      ( ? [X2] :
          ( ! [X3] :
              ( ~ in(X3,X2)
              | ~ in(X3,X1) )
          & in(X2,X1) )
     => ( ! [X3] :
            ( ~ in(X3,sK18(X1))
            | ~ in(X3,X1) )
        & in(sK18(X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f124,plain,
    ! [X0,X1] :
      ( ( ! [X3] :
            ( ~ in(X3,sK18(X1))
            | ~ in(X3,X1) )
        & in(sK18(X1),X1) )
      | ~ in(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f84,f123]) ).

fof(f127,plain,
    ! [X0] :
      ( epsilon_transitive(X0)
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f137,plain,
    ! [X2,X0] :
      ( subset(X2,X0)
      | ~ in(X2,X0)
      | ~ epsilon_transitive(X0) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f138,plain,
    ! [X0] :
      ( epsilon_transitive(X0)
      | in(sK0(X0),X0) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f140,plain,
    ! [X0] : element(sK1(X0),X0),
    inference(cnf_transformation,[],[f91]) ).

fof(f150,plain,
    empty(empty_set),
    inference(cnf_transformation,[],[f14]) ).

fof(f184,plain,
    ! [X0,X1] :
      ( ordinal_subset(X0,X1)
      | ~ subset(X0,X1)
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f118]) ).

fof(f186,plain,
    ! [X0] : subset(X0,X0),
    inference(cnf_transformation,[],[f44]) ).

fof(f188,plain,
    ! [X0,X1] :
      ( ordinal(X0)
      | ~ in(X0,X1)
      | ~ ordinal(X1) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f189,plain,
    ! [X0,X1] :
      ( in(X1,X0)
      | X0 = X1
      | in(X0,X1)
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f190,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(cnf_transformation,[],[f76]) ).

fof(f191,plain,
    ordinal(sK16),
    inference(cnf_transformation,[],[f121]) ).

fof(f192,plain,
    subset(sK15,sK16),
    inference(cnf_transformation,[],[f121]) ).

fof(f193,plain,
    empty_set != sK15,
    inference(cnf_transformation,[],[f121]) ).

fof(f194,plain,
    ! [X2] :
      ( ordinal(sK17(X2))
      | ~ in(X2,sK15)
      | ~ ordinal(X2) ),
    inference(cnf_transformation,[],[f121]) ).

fof(f195,plain,
    ! [X2] :
      ( in(sK17(X2),sK15)
      | ~ in(X2,sK15)
      | ~ ordinal(X2) ),
    inference(cnf_transformation,[],[f121]) ).

fof(f196,plain,
    ! [X2] :
      ( ~ ordinal_subset(X2,sK17(X2))
      | ~ in(X2,sK15)
      | ~ ordinal(X2) ),
    inference(cnf_transformation,[],[f121]) ).

fof(f198,plain,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f122]) ).

fof(f199,plain,
    ! [X2,X0,X1] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f80]) ).

fof(f200,plain,
    ! [X2,X0,X1] :
      ( ~ empty(X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f81]) ).

fof(f203,plain,
    ! [X0,X1] :
      ( in(sK18(X1),X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f124]) ).

fof(f204,plain,
    ! [X3,X0,X1] :
      ( ~ in(X3,sK18(X1))
      | ~ in(X3,X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f124]) ).

fof(f205,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | X0 = X1
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f85]) ).

cnf(c_52,plain,
    ( ~ ordinal(X0)
    | epsilon_transitive(X0) ),
    inference(cnf_transformation,[],[f127]) ).

cnf(c_60,plain,
    ( in(sK0(X0),X0)
    | epsilon_transitive(X0) ),
    inference(cnf_transformation,[],[f138]) ).

cnf(c_61,plain,
    ( ~ in(X0,X1)
    | ~ epsilon_transitive(X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f137]) ).

cnf(c_62,plain,
    element(sK1(X0),X0),
    inference(cnf_transformation,[],[f140]) ).

cnf(c_73,plain,
    empty(empty_set),
    inference(cnf_transformation,[],[f150]) ).

cnf(c_105,plain,
    ( ~ subset(X0,X1)
    | ~ ordinal(X0)
    | ~ ordinal(X1)
    | ordinal_subset(X0,X1) ),
    inference(cnf_transformation,[],[f184]) ).

cnf(c_108,plain,
    subset(X0,X0),
    inference(cnf_transformation,[],[f186]) ).

cnf(c_110,plain,
    ( ~ in(X0,X1)
    | ~ ordinal(X1)
    | ordinal(X0) ),
    inference(cnf_transformation,[],[f188]) ).

cnf(c_111,plain,
    ( ~ ordinal(X0)
    | ~ ordinal(X1)
    | X0 = X1
    | in(X0,X1)
    | in(X1,X0) ),
    inference(cnf_transformation,[],[f189]) ).

cnf(c_112,plain,
    ( ~ element(X0,X1)
    | in(X0,X1)
    | empty(X1) ),
    inference(cnf_transformation,[],[f190]) ).

cnf(c_113,negated_conjecture,
    ( ~ ordinal_subset(X0,sK17(X0))
    | ~ in(X0,sK15)
    | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f196]) ).

cnf(c_114,negated_conjecture,
    ( ~ in(X0,sK15)
    | ~ ordinal(X0)
    | in(sK17(X0),sK15) ),
    inference(cnf_transformation,[],[f195]) ).

cnf(c_115,negated_conjecture,
    ( ~ in(X0,sK15)
    | ~ ordinal(X0)
    | ordinal(sK17(X0)) ),
    inference(cnf_transformation,[],[f194]) ).

cnf(c_116,negated_conjecture,
    empty_set != sK15,
    inference(cnf_transformation,[],[f193]) ).

cnf(c_117,negated_conjecture,
    subset(sK15,sK16),
    inference(cnf_transformation,[],[f192]) ).

cnf(c_118,negated_conjecture,
    ordinal(sK16),
    inference(cnf_transformation,[],[f191]) ).

cnf(c_119,plain,
    ( ~ subset(X0,X1)
    | element(X0,powerset(X1)) ),
    inference(cnf_transformation,[],[f198]) ).

cnf(c_121,plain,
    ( ~ element(X0,powerset(X1))
    | ~ in(X2,X0)
    | element(X2,X1) ),
    inference(cnf_transformation,[],[f199]) ).

cnf(c_122,plain,
    ( ~ element(X0,powerset(X1))
    | ~ in(X2,X0)
    | ~ empty(X1) ),
    inference(cnf_transformation,[],[f200]) ).

cnf(c_125,plain,
    ( ~ in(X0,sK18(X1))
    | ~ in(X0,X1)
    | ~ in(X2,X1) ),
    inference(cnf_transformation,[],[f204]) ).

cnf(c_126,plain,
    ( ~ in(X0,X1)
    | in(sK18(X1),X1) ),
    inference(cnf_transformation,[],[f203]) ).

cnf(c_127,plain,
    ( ~ empty(X0)
    | ~ empty(X1)
    | X0 = X1 ),
    inference(cnf_transformation,[],[f205]) ).

cnf(c_144,plain,
    ( ~ subset(X0,X1)
    | element(X0,powerset(X1)) ),
    inference(prop_impl_just,[status(thm)],[c_119]) ).

cnf(c_286,plain,
    ( ~ in(X0,X1)
    | ~ subset(X1,X2)
    | element(X0,X2) ),
    inference(bin_hyper_res,[status(thm)],[c_121,c_144]) ).

cnf(c_287,plain,
    ( ~ in(X0,X1)
    | ~ subset(X1,X2)
    | ~ empty(X2) ),
    inference(bin_hyper_res,[status(thm)],[c_122,c_144]) ).

cnf(c_836,plain,
    ( X0 != X1
    | X1 != X2
    | ~ ordinal(X0)
    | ~ ordinal(X2)
    | ordinal_subset(X0,X2) ),
    inference(resolution_lifted,[status(thm)],[c_105,c_108]) ).

cnf(c_837,plain,
    ( ~ ordinal(X0)
    | ordinal_subset(X0,X0) ),
    inference(unflattening,[status(thm)],[c_836]) ).

cnf(c_1028,plain,
    ( ~ ordinal(X0)
    | ordinal_subset(X0,X0) ),
    inference(prop_impl_just,[status(thm)],[c_837]) ).

cnf(c_1732,plain,
    ( X0 != X1
    | ~ ordinal_subset(X2,X1)
    | ordinal_subset(X2,X0) ),
    theory(equality) ).

cnf(c_2468,plain,
    ( ~ ordinal_subset(sK18(sK15),sK17(sK18(sK15)))
    | ~ in(sK18(sK15),sK15)
    | ~ ordinal(sK18(sK15)) ),
    inference(instantiation,[status(thm)],[c_113]) ).

cnf(c_2471,plain,
    ( ~ empty(empty_set)
    | ~ empty(sK15)
    | empty_set = sK15 ),
    inference(instantiation,[status(thm)],[c_127]) ).

cnf(c_2474,plain,
    ( ~ in(sK18(sK15),sK15)
    | ~ ordinal(sK18(sK15))
    | in(sK17(sK18(sK15)),sK15) ),
    inference(instantiation,[status(thm)],[c_114]) ).

cnf(c_2476,plain,
    ( ~ in(sK18(sK15),sK15)
    | ~ ordinal(sK18(sK15))
    | ordinal(sK17(sK18(sK15))) ),
    inference(instantiation,[status(thm)],[c_115]) ).

cnf(c_2478,plain,
    ( ~ in(X0,sK15)
    | ~ subset(sK15,sK16)
    | ~ empty(sK16) ),
    inference(instantiation,[status(thm)],[c_287]) ).

cnf(c_2480,plain,
    ( ~ in(sK18(sK15),X0)
    | ~ ordinal(X0)
    | ordinal(sK18(sK15)) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_2487,plain,
    ( ~ element(X0,sK15)
    | in(X0,sK15)
    | empty(sK15) ),
    inference(instantiation,[status(thm)],[c_112]) ).

cnf(c_2491,plain,
    ( ~ element(X0,sK16)
    | in(X0,sK16)
    | empty(sK16) ),
    inference(instantiation,[status(thm)],[c_112]) ).

cnf(c_2550,plain,
    ( ~ in(X0,X1)
    | ~ subset(X1,sK16)
    | element(X0,sK16) ),
    inference(instantiation,[status(thm)],[c_286]) ).

cnf(c_2552,plain,
    ( ~ element(sK1(sK15),sK15)
    | in(sK1(sK15),sK15)
    | empty(sK15) ),
    inference(instantiation,[status(thm)],[c_2487]) ).

cnf(c_2606,plain,
    element(sK1(sK15),sK15),
    inference(instantiation,[status(thm)],[c_62]) ).

cnf(c_2661,plain,
    ( ~ element(sK18(sK15),sK16)
    | in(sK18(sK15),sK16)
    | empty(sK16) ),
    inference(instantiation,[status(thm)],[c_2491]) ).

cnf(c_2731,plain,
    ( ~ in(sK1(sK15),sK15)
    | in(sK18(sK15),sK15) ),
    inference(instantiation,[status(thm)],[c_126]) ).

cnf(c_2733,plain,
    ( ~ in(sK1(sK15),sK15)
    | ~ subset(sK15,sK16)
    | ~ empty(sK16) ),
    inference(instantiation,[status(thm)],[c_2478]) ).

cnf(c_2830,plain,
    ( ~ subset(sK18(sK15),sK17(sK18(sK15)))
    | ~ ordinal(sK17(sK18(sK15)))
    | ~ ordinal(sK18(sK15))
    | ordinal_subset(sK18(sK15),sK17(sK18(sK15))) ),
    inference(instantiation,[status(thm)],[c_105]) ).

cnf(c_2832,plain,
    ( sK17(sK18(sK15)) != X0
    | ~ ordinal_subset(sK18(sK15),X0)
    | ordinal_subset(sK18(sK15),sK17(sK18(sK15))) ),
    inference(instantiation,[status(thm)],[c_1732]) ).

cnf(c_2843,plain,
    ( ~ in(sK17(sK18(sK15)),sK15)
    | ~ ordinal(sK17(sK18(sK15)))
    | in(sK17(sK17(sK18(sK15))),sK15) ),
    inference(instantiation,[status(thm)],[c_114]) ).

cnf(c_2880,plain,
    ( ~ in(sK18(sK15),sK15)
    | ~ subset(sK15,sK16)
    | element(sK18(sK15),sK16) ),
    inference(instantiation,[status(thm)],[c_2550]) ).

cnf(c_3191,plain,
    ( ~ in(sK18(sK15),sK16)
    | ~ ordinal(sK16)
    | ordinal(sK18(sK15)) ),
    inference(instantiation,[status(thm)],[c_2480]) ).

cnf(c_3477,plain,
    ( in(sK18(X0),X0)
    | epsilon_transitive(X0) ),
    inference(superposition,[status(thm)],[c_60,c_126]) ).

cnf(c_3602,plain,
    ( ~ ordinal(sK18(sK15))
    | ordinal(sK17(sK18(sK15)))
    | epsilon_transitive(sK15) ),
    inference(superposition,[status(thm)],[c_3477,c_115]) ).

cnf(c_3628,plain,
    ( ~ in(sK18(sK15),sK17(sK18(sK15)))
    | ~ epsilon_transitive(sK17(sK18(sK15)))
    | subset(sK18(sK15),sK17(sK18(sK15))) ),
    inference(instantiation,[status(thm)],[c_61]) ).

cnf(c_3712,plain,
    ( ~ in(sK17(sK17(sK18(sK15))),sK15)
    | ~ in(X0,sK18(sK15))
    | ~ in(X0,sK15) ),
    inference(instantiation,[status(thm)],[c_125]) ).

cnf(c_3748,plain,
    ordinal(sK17(sK18(sK15))),
    inference(global_subsumption_just,[status(thm)],[c_3602,c_118,c_73,c_117,c_116,c_2471,c_2476,c_2552,c_2606,c_2661,c_2731,c_2733,c_2880,c_3191]) ).

cnf(c_3750,plain,
    epsilon_transitive(sK17(sK18(sK15))),
    inference(superposition,[status(thm)],[c_3748,c_52]) ).

cnf(c_3770,plain,
    ( sK17(sK18(sK15)) != sK18(sK15)
    | ~ ordinal_subset(sK18(sK15),sK18(sK15))
    | ordinal_subset(sK18(sK15),sK17(sK18(sK15))) ),
    inference(instantiation,[status(thm)],[c_2832]) ).

cnf(c_4699,plain,
    ( ~ ordinal(sK17(sK18(sK15)))
    | ~ ordinal(X0)
    | sK17(sK18(sK15)) = X0
    | in(sK17(sK18(sK15)),X0)
    | in(X0,sK17(sK18(sK15))) ),
    inference(instantiation,[status(thm)],[c_111]) ).

cnf(c_4838,plain,
    ( ~ ordinal(sK18(sK15))
    | ordinal_subset(sK18(sK15),sK18(sK15)) ),
    inference(instantiation,[status(thm)],[c_1028]) ).

cnf(c_5343,plain,
    ( ~ in(sK17(sK17(sK18(sK15))),sK15)
    | ~ in(sK17(sK18(sK15)),sK18(sK15))
    | ~ in(sK17(sK18(sK15)),sK15) ),
    inference(instantiation,[status(thm)],[c_3712]) ).

cnf(c_13048,plain,
    ( ~ ordinal(sK17(sK18(sK15)))
    | ~ ordinal(sK18(sK15))
    | sK17(sK18(sK15)) = sK18(sK15)
    | in(sK17(sK18(sK15)),sK18(sK15))
    | in(sK18(sK15),sK17(sK18(sK15))) ),
    inference(instantiation,[status(thm)],[c_4699]) ).

cnf(c_13049,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_13048,c_5343,c_4838,c_3770,c_3750,c_3628,c_3191,c_2880,c_2843,c_2830,c_2733,c_2731,c_2661,c_2606,c_2552,c_2476,c_2474,c_2471,c_2468,c_116,c_117,c_73,c_118]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU235+3 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13  % Command  : run_iprover %s %d THM
% 0.14/0.35  % Computer : n007.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu May  2 17:22:20 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.21/0.48  Running first-order theorem proving
% 0.21/0.48  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.09/1.16  % SZS status Started for theBenchmark.p
% 4.09/1.16  % SZS status Theorem for theBenchmark.p
% 4.09/1.16  
% 4.09/1.16  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 4.09/1.16  
% 4.09/1.16  ------  iProver source info
% 4.09/1.16  
% 4.09/1.16  git: date: 2024-05-02 19:28:25 +0000
% 4.09/1.16  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 4.09/1.16  git: non_committed_changes: false
% 4.09/1.16  
% 4.09/1.16  ------ Parsing...
% 4.09/1.16  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 4.09/1.16  
% 4.09/1.16  ------ Preprocessing... sup_sim: 0  sf_s  rm: 22 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 0  sf_s  rm: 4 0s  sf_e  pe_s  pe_e 
% 4.09/1.16  
% 4.09/1.16  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 4.09/1.16  
% 4.09/1.16  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 4.09/1.16  ------ Proving...
% 4.09/1.16  ------ Problem Properties 
% 4.09/1.16  
% 4.09/1.16  
% 4.09/1.16  clauses                                 48
% 4.09/1.16  conjectures                             6
% 4.09/1.16  EPR                                     38
% 4.09/1.16  Horn                                    44
% 4.09/1.16  unary                                   21
% 4.09/1.16  binary                                  13
% 4.09/1.16  lits                                    94
% 4.09/1.16  lits eq                                 4
% 4.09/1.16  fd_pure                                 0
% 4.09/1.16  fd_pseudo                               0
% 4.09/1.16  fd_cond                                 1
% 4.09/1.16  fd_pseudo_cond                          2
% 4.09/1.16  AC symbols                              0
% 4.09/1.16  
% 4.09/1.16  ------ Input Options Time Limit: Unbounded
% 4.09/1.16  
% 4.09/1.16  
% 4.09/1.16  ------ 
% 4.09/1.16  Current options:
% 4.09/1.16  ------ 
% 4.09/1.16  
% 4.09/1.16  
% 4.09/1.16  
% 4.09/1.16  
% 4.09/1.16  ------ Proving...
% 4.09/1.16  
% 4.09/1.16  
% 4.09/1.16  % SZS status Theorem for theBenchmark.p
% 4.09/1.16  
% 4.09/1.16  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.09/1.16  
% 4.09/1.17  
%------------------------------------------------------------------------------