TSTP Solution File: SEU235+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU235+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n006.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 : Sun May  5 09:29:57 EDT 2024

% Result   : Theorem 0.16s 0.37s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   23
% Syntax   : Number of formulae    :  105 (  27 unt;   0 def)
%            Number of atoms       :  319 (  17 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  375 ( 161   ~; 115   |;  66   &)
%                                         (   9 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   14 (  12 usr;   2 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   3 con; 0-2 aty)
%            Number of variables   :  180 ( 159   !;  21   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2439,plain,
    $false,
    inference(subsumption_resolution,[],[f2419,f1984]) ).

fof(f1984,plain,
    ordinal_subset(sK7(sK3),sK7(sK3)),
    inference(unit_resulting_resolution,[],[f1960,f220]) ).

fof(f220,plain,
    ! [X0] :
      ( ~ ordinal(X0)
      | ordinal_subset(X0,X0) ),
    inference(subsumption_resolution,[],[f213,f214]) ).

fof(f214,plain,
    ! [X1] :
      ( ~ ordinal(X1)
      | ~ sP20 ),
    inference(general_splitting,[],[f172,f213_D]) ).

fof(f172,plain,
    ! [X0,X1] :
      ( ordinal_subset(X0,X0)
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f76]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( ordinal_subset(X0,X0)
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(flattening,[],[f75]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( ordinal_subset(X0,X0)
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f31,axiom,
    ! [X0,X1] :
      ( ( ordinal(X1)
        & ordinal(X0) )
     => ordinal_subset(X0,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_ordinal1) ).

fof(f213,plain,
    ! [X0] :
      ( ordinal_subset(X0,X0)
      | ~ ordinal(X0)
      | sP20 ),
    inference(cnf_transformation,[],[f213_D]) ).

fof(f213_D,plain,
    ( ! [X0] :
        ( ordinal_subset(X0,X0)
        | ~ ordinal(X0) )
  <=> ~ sP20 ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP20])]) ).

fof(f1960,plain,
    ordinal(sK7(sK3)),
    inference(unit_resulting_resolution,[],[f135,f1918,f168]) ).

fof(f168,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | ordinal(X0)
      | ~ ordinal(X1) ),
    inference(cnf_transformation,[],[f70]) ).

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

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

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

fof(f1918,plain,
    in(sK7(sK3),sK4),
    inference(unit_resulting_resolution,[],[f662,f1863,f169]) ).

fof(f169,plain,
    ! [X0,X1] :
      ( ~ element(X0,X1)
      | empty(X1)
      | in(X0,X1) ),
    inference(cnf_transformation,[],[f72]) ).

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

fof(f71,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(ennf_transformation,[],[f36]) ).

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

fof(f1863,plain,
    element(sK7(sK3),sK4),
    inference(unit_resulting_resolution,[],[f479,f388,f182]) ).

fof(f182,plain,
    ! [X2,X0,X1] :
      ( ~ element(X1,powerset(X2))
      | element(X0,X2)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f85]) ).

fof(f85,plain,
    ! [X0,X1,X2] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(flattening,[],[f84]) ).

fof(f84,plain,
    ! [X0,X1,X2] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f40]) ).

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(f388,plain,
    element(sK3,powerset(sK4)),
    inference(unit_resulting_resolution,[],[f136,f177]) ).

fof(f177,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | element(X0,powerset(X1)) ),
    inference(cnf_transformation,[],[f105]) ).

fof(f105,plain,
    ! [X0,X1] :
      ( ( element(X0,powerset(X1))
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ~ element(X0,powerset(X1)) ) ),
    inference(nnf_transformation,[],[f39]) ).

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

fof(f136,plain,
    subset(sK3,sK4),
    inference(cnf_transformation,[],[f96]) ).

fof(f96,plain,
    ( ! [X2] :
        ( sP0(X2,sK3)
        | ~ in(X2,sK3)
        | ~ ordinal(X2) )
    & empty_set != sK3
    & subset(sK3,sK4)
    & ordinal(sK4) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f88,f95]) ).

fof(f95,plain,
    ( ? [X0,X1] :
        ( ! [X2] :
            ( sP0(X2,X0)
            | ~ in(X2,X0)
            | ~ ordinal(X2) )
        & empty_set != X0
        & subset(X0,X1)
        & ordinal(X1) )
   => ( ! [X2] :
          ( sP0(X2,sK3)
          | ~ in(X2,sK3)
          | ~ ordinal(X2) )
      & empty_set != sK3
      & subset(sK3,sK4)
      & ordinal(sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f88,plain,
    ? [X0,X1] :
      ( ! [X2] :
          ( sP0(X2,X0)
          | ~ in(X2,X0)
          | ~ ordinal(X2) )
      & empty_set != X0
      & subset(X0,X1)
      & ordinal(X1) ),
    inference(definition_folding,[],[f56,f87]) ).

fof(f87,plain,
    ! [X2,X0] :
      ( ? [X3] :
          ( ~ ordinal_subset(X2,X3)
          & in(X3,X0)
          & ordinal(X3) )
      | ~ sP0(X2,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f56,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,[],[f55]) ).

fof(f55,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,[],[f38]) ).

fof(f38,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,[],[f37]) ).

fof(f37,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(f479,plain,
    in(sK7(sK3),sK3),
    inference(unit_resulting_resolution,[],[f465,f180]) ).

fof(f180,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | in(sK7(X1),X1) ),
    inference(cnf_transformation,[],[f107]) ).

fof(f107,plain,
    ! [X0,X1] :
      ( ( ! [X3] :
            ( ~ in(X3,sK7(X1))
            | ~ in(X3,X1) )
        & in(sK7(X1),X1) )
      | ~ in(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f83,f106]) ).

fof(f106,plain,
    ! [X1] :
      ( ? [X2] :
          ( ! [X3] :
              ( ~ in(X3,X2)
              | ~ in(X3,X1) )
          & in(X2,X1) )
     => ( ! [X3] :
            ( ~ in(X3,sK7(X1))
            | ~ in(X3,X1) )
        & in(sK7(X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ! [X3] :
              ( ~ in(X3,X2)
              | ~ in(X3,X1) )
          & in(X2,X1) )
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f44]) ).

fof(f44,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(f465,plain,
    in(sK6(sK3),sK3),
    inference(unit_resulting_resolution,[],[f294,f166,f169]) ).

fof(f166,plain,
    ! [X0] : element(sK6(X0),X0),
    inference(cnf_transformation,[],[f103]) ).

fof(f103,plain,
    ! [X0] : element(sK6(X0),X0),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f13,f102]) ).

fof(f102,plain,
    ! [X0] :
      ( ? [X1] : element(X1,X0)
     => element(sK6(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f13,axiom,
    ! [X0] :
    ? [X1] : element(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).

fof(f294,plain,
    ~ empty(sK3),
    inference(unit_resulting_resolution,[],[f137,f155]) ).

fof(f155,plain,
    ! [X0] :
      ( ~ empty(X0)
      | empty_set = X0 ),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f42]) ).

fof(f42,axiom,
    ! [X0] :
      ( empty(X0)
     => empty_set = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

fof(f137,plain,
    empty_set != sK3,
    inference(cnf_transformation,[],[f96]) ).

fof(f662,plain,
    ~ empty(sK4),
    inference(unit_resulting_resolution,[],[f481,f388,f217]) ).

fof(f217,plain,
    ! [X2,X1] :
      ( ~ element(X1,powerset(X2))
      | ~ empty(X2)
      | sP22(X1) ),
    inference(cnf_transformation,[],[f217_D]) ).

fof(f217_D,plain,
    ! [X1] :
      ( ! [X2] :
          ( ~ element(X1,powerset(X2))
          | ~ empty(X2) )
    <=> ~ sP22(X1) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP22])]) ).

fof(f481,plain,
    ~ sP22(sK3),
    inference(unit_resulting_resolution,[],[f465,f218]) ).

fof(f218,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | ~ sP22(X1) ),
    inference(general_splitting,[],[f183,f217_D]) ).

fof(f183,plain,
    ! [X2,X0,X1] :
      ( ~ empty(X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f86]) ).

fof(f86,plain,
    ! [X0,X1,X2] :
      ( ~ empty(X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f41]) ).

fof(f41,axiom,
    ! [X0,X1,X2] :
      ~ ( empty(X2)
        & element(X1,powerset(X2))
        & in(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).

fof(f135,plain,
    ordinal(sK4),
    inference(cnf_transformation,[],[f96]) ).

fof(f2419,plain,
    ~ ordinal_subset(sK7(sK3),sK7(sK3)),
    inference(superposition,[],[f2013,f2400]) ).

fof(f2400,plain,
    sK7(sK3) = sK2(sK7(sK3),sK3),
    inference(unit_resulting_resolution,[],[f1960,f2015,f2135,f2359,f152]) ).

fof(f152,plain,
    ! [X0,X1] :
      ( ~ ordinal(X1)
      | X0 = X1
      | in(X0,X1)
      | in(X1,X0)
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f59,plain,
    ! [X0] :
      ( ! [X1] :
          ( in(X1,X0)
          | X0 = X1
          | in(X0,X1)
          | ~ ordinal(X1) )
      | ~ ordinal(X0) ),
    inference(flattening,[],[f58]) ).

fof(f58,plain,
    ! [X0] :
      ( ! [X1] :
          ( in(X1,X0)
          | X0 = X1
          | in(X0,X1)
          | ~ ordinal(X1) )
      | ~ ordinal(X0) ),
    inference(ennf_transformation,[],[f35]) ).

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(f2359,plain,
    ~ in(sK7(sK3),sK2(sK7(sK3),sK3)),
    inference(unit_resulting_resolution,[],[f2054,f2330,f163]) ).

fof(f163,plain,
    ! [X2,X0] :
      ( ~ in(X2,X0)
      | subset(X2,X0)
      | ~ epsilon_transitive(X0) ),
    inference(cnf_transformation,[],[f101]) ).

fof(f101,plain,
    ! [X0] :
      ( ( epsilon_transitive(X0)
        | ( ~ subset(sK5(X0),X0)
          & in(sK5(X0),X0) ) )
      & ( ! [X2] :
            ( subset(X2,X0)
            | ~ in(X2,X0) )
        | ~ epsilon_transitive(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f99,f100]) ).

fof(f100,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ subset(X1,X0)
          & in(X1,X0) )
     => ( ~ subset(sK5(X0),X0)
        & in(sK5(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f99,plain,
    ! [X0] :
      ( ( epsilon_transitive(X0)
        | ? [X1] :
            ( ~ subset(X1,X0)
            & in(X1,X0) ) )
      & ( ! [X2] :
            ( subset(X2,X0)
            | ~ in(X2,X0) )
        | ~ epsilon_transitive(X0) ) ),
    inference(rectify,[],[f98]) ).

fof(f98,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,[],[f68]) ).

fof(f68,plain,
    ! [X0] :
      ( epsilon_transitive(X0)
    <=> ! [X1] :
          ( subset(X1,X0)
          | ~ in(X1,X0) ) ),
    inference(ennf_transformation,[],[f9]) ).

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

fof(f2330,plain,
    ~ subset(sK7(sK3),sK2(sK7(sK3),sK3)),
    inference(unit_resulting_resolution,[],[f1960,f2015,f2013,f175]) ).

fof(f175,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | ordinal_subset(X0,X1)
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f104]) ).

fof(f104,plain,
    ! [X0,X1] :
      ( ( ( ordinal_subset(X0,X1)
          | ~ subset(X0,X1) )
        & ( subset(X0,X1)
          | ~ ordinal_subset(X0,X1) ) )
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(nnf_transformation,[],[f80]) ).

fof(f80,plain,
    ! [X0,X1] :
      ( ( ordinal_subset(X0,X1)
      <=> subset(X0,X1) )
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(flattening,[],[f79]) ).

fof(f79,plain,
    ! [X0,X1] :
      ( ( ordinal_subset(X0,X1)
      <=> subset(X0,X1) )
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f30,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(f2054,plain,
    epsilon_transitive(sK2(sK7(sK3),sK3)),
    inference(unit_resulting_resolution,[],[f2015,f150]) ).

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

fof(f57,plain,
    ! [X0] :
      ( ( epsilon_connected(X0)
        & epsilon_transitive(X0) )
      | ~ ordinal(X0) ),
    inference(ennf_transformation,[],[f3]) ).

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

fof(f2135,plain,
    ~ in(sK2(sK7(sK3),sK3),sK7(sK3)),
    inference(unit_resulting_resolution,[],[f2014,f219]) ).

fof(f219,plain,
    ! [X3,X1] :
      ( ~ in(X3,sK7(X1))
      | ~ in(X3,X1) ),
    inference(subsumption_resolution,[],[f215,f216]) ).

fof(f216,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | ~ sP21(X1) ),
    inference(general_splitting,[],[f181,f215_D]) ).

fof(f181,plain,
    ! [X3,X0,X1] :
      ( ~ in(X3,sK7(X1))
      | ~ in(X3,X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f107]) ).

fof(f215,plain,
    ! [X3,X1] :
      ( ~ in(X3,sK7(X1))
      | ~ in(X3,X1)
      | sP21(X1) ),
    inference(cnf_transformation,[],[f215_D]) ).

fof(f215_D,plain,
    ! [X1] :
      ( ! [X3] :
          ( ~ in(X3,sK7(X1))
          | ~ in(X3,X1) )
    <=> ~ sP21(X1) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP21])]) ).

fof(f2014,plain,
    in(sK2(sK7(sK3),sK3),sK3),
    inference(unit_resulting_resolution,[],[f1979,f133]) ).

fof(f133,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | in(sK2(X0,X1),X1) ),
    inference(cnf_transformation,[],[f94]) ).

fof(f94,plain,
    ! [X0,X1] :
      ( ( ~ ordinal_subset(X0,sK2(X0,X1))
        & in(sK2(X0,X1),X1)
        & ordinal(sK2(X0,X1)) )
      | ~ sP0(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f92,f93]) ).

fof(f93,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ ordinal_subset(X0,X2)
          & in(X2,X1)
          & ordinal(X2) )
     => ( ~ ordinal_subset(X0,sK2(X0,X1))
        & in(sK2(X0,X1),X1)
        & ordinal(sK2(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f92,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ ordinal_subset(X0,X2)
          & in(X2,X1)
          & ordinal(X2) )
      | ~ sP0(X0,X1) ),
    inference(rectify,[],[f91]) ).

fof(f91,plain,
    ! [X2,X0] :
      ( ? [X3] :
          ( ~ ordinal_subset(X2,X3)
          & in(X3,X0)
          & ordinal(X3) )
      | ~ sP0(X2,X0) ),
    inference(nnf_transformation,[],[f87]) ).

fof(f1979,plain,
    sP0(sK7(sK3),sK3),
    inference(unit_resulting_resolution,[],[f479,f1960,f138]) ).

fof(f138,plain,
    ! [X2] :
      ( ~ in(X2,sK3)
      | sP0(X2,sK3)
      | ~ ordinal(X2) ),
    inference(cnf_transformation,[],[f96]) ).

fof(f2015,plain,
    ordinal(sK2(sK7(sK3),sK3)),
    inference(unit_resulting_resolution,[],[f1979,f132]) ).

fof(f132,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | ordinal(sK2(X0,X1)) ),
    inference(cnf_transformation,[],[f94]) ).

fof(f2013,plain,
    ~ ordinal_subset(sK7(sK3),sK2(sK7(sK3),sK3)),
    inference(unit_resulting_resolution,[],[f1979,f134]) ).

fof(f134,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | ~ ordinal_subset(X0,sK2(X0,X1)) ),
    inference(cnf_transformation,[],[f94]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.09  % Problem    : SEU235+1 : TPTP v8.1.2. Released v3.3.0.
% 0.09/0.11  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31  % Computer : n006.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 May  3 10:57:49 EDT 2024
% 0.10/0.31  % CPUTime    : 
% 0.10/0.31  % (17644)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.32  % (17649)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.32  TRYING [1]
% 0.16/0.32  TRYING [2]
% 0.16/0.32  TRYING [3]
% 0.16/0.32  TRYING [4]
% 0.16/0.32  % (17648)WARNING: value z3 for option sas not known
% 0.16/0.33  TRYING [5]
% 0.16/0.33  % (17646)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.33  % (17650)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.16/0.33  % (17648)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.16/0.33  % (17647)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.33  % (17651)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.16/0.33  % (17653)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.16/0.33  TRYING [6]
% 0.16/0.33  TRYING [1]
% 0.16/0.33  TRYING [2]
% 0.16/0.33  TRYING [3]
% 0.16/0.34  TRYING [7]
% 0.16/0.34  TRYING [4]
% 0.16/0.35  TRYING [8]
% 0.16/0.36  % (17653)First to succeed.
% 0.16/0.36  TRYING [9]
% 0.16/0.36  TRYING [5]
% 0.16/0.37  % (17653)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-17644"
% 0.16/0.37  % (17653)Refutation found. Thanks to Tanya!
% 0.16/0.37  % SZS status Theorem for theBenchmark
% 0.16/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.37  % (17653)------------------------------
% 0.16/0.37  % (17653)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.16/0.37  % (17653)Termination reason: Refutation
% 0.16/0.37  
% 0.16/0.37  % (17653)Memory used [KB]: 1406
% 0.16/0.37  % (17653)Time elapsed: 0.040 s
% 0.16/0.37  % (17653)Instructions burned: 74 (million)
% 0.16/0.37  % (17644)Success in time 0.056 s
%------------------------------------------------------------------------------