TSTP Solution File: NUM397+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM397+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n023.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 : Tue May 21 01:57:19 EDT 2024

% Result   : Theorem 4.43s 1.05s
% Output   : Refutation 4.43s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   24
% Syntax   : Number of formulae    :  135 (  26 unt;   0 def)
%            Number of atoms       :  408 (  21 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  429 ( 156   ~; 166   |;  77   &)
%                                         (  11 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   12 (  10 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   1 con; 0-2 aty)
%            Number of variables   :  190 ( 169   !;  21   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f28311,plain,
    $false,
    inference(subsumption_resolution,[],[f28290,f27470]) ).

fof(f27470,plain,
    in(sK6(union(sK3)),sK9(sK3,sK6(union(sK3)))),
    inference(unit_resulting_resolution,[],[f27433,f1267]) ).

fof(f1267,plain,
    ! [X0] :
      ( in(sK6(union(X0)),sK9(X0,sK6(union(X0))))
      | epsilon_connected(union(X0)) ),
    inference(resolution,[],[f1223,f196]) ).

fof(f196,plain,
    ! [X0,X1] :
      ( ~ sP1(X0,X1)
      | in(X1,sK9(X0,X1)) ),
    inference(cnf_transformation,[],[f116]) ).

fof(f116,plain,
    ! [X0,X1] :
      ( ( sP1(X0,X1)
        | ! [X2] :
            ( ~ in(X2,X0)
            | ~ in(X1,X2) ) )
      & ( ( in(sK9(X0,X1),X0)
          & in(X1,sK9(X0,X1)) )
        | ~ sP1(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f114,f115]) ).

fof(f115,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( in(X3,X0)
          & in(X1,X3) )
     => ( in(sK9(X0,X1),X0)
        & in(X1,sK9(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f114,plain,
    ! [X0,X1] :
      ( ( sP1(X0,X1)
        | ! [X2] :
            ( ~ in(X2,X0)
            | ~ in(X1,X2) ) )
      & ( ? [X3] :
            ( in(X3,X0)
            & in(X1,X3) )
        | ~ sP1(X0,X1) ) ),
    inference(rectify,[],[f113]) ).

fof(f113,plain,
    ! [X0,X2] :
      ( ( sP1(X0,X2)
        | ! [X3] :
            ( ~ in(X3,X0)
            | ~ in(X2,X3) ) )
      & ( ? [X3] :
            ( in(X3,X0)
            & in(X2,X3) )
        | ~ sP1(X0,X2) ) ),
    inference(nnf_transformation,[],[f90]) ).

fof(f90,plain,
    ! [X0,X2] :
      ( sP1(X0,X2)
    <=> ? [X3] :
          ( in(X3,X0)
          & in(X2,X3) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f1223,plain,
    ! [X0] :
      ( sP1(X0,sK6(union(X0)))
      | epsilon_connected(union(X0)) ),
    inference(resolution,[],[f930,f174]) ).

fof(f174,plain,
    ! [X0] :
      ( in(sK6(X0),X0)
      | epsilon_connected(X0) ),
    inference(cnf_transformation,[],[f103]) ).

fof(f103,plain,
    ! [X0] :
      ( ( epsilon_connected(X0)
        | ( ~ in(sK6(X0),sK5(X0))
          & sK5(X0) != sK6(X0)
          & ~ in(sK5(X0),sK6(X0))
          & in(sK6(X0),X0)
          & in(sK5(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,[sK5,sK6])],[f101,f102]) ).

fof(f102,plain,
    ! [X0] :
      ( ? [X1,X2] :
          ( ~ in(X2,X1)
          & X1 != X2
          & ~ in(X1,X2)
          & in(X2,X0)
          & in(X1,X0) )
     => ( ~ in(sK6(X0),sK5(X0))
        & sK5(X0) != sK6(X0)
        & ~ in(sK5(X0),sK6(X0))
        & in(sK6(X0),X0)
        & in(sK5(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f101,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,[],[f100]) ).

fof(f100,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,[],[f69]) ).

fof(f69,plain,
    ! [X0] :
      ( epsilon_connected(X0)
    <=> ! [X1,X2] :
          ( in(X2,X1)
          | X1 = X2
          | in(X1,X2)
          | ~ in(X2,X0)
          | ~ in(X1,X0) ) ),
    inference(ennf_transformation,[],[f10]) ).

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

fof(f930,plain,
    ! [X0,X1] :
      ( ~ in(X0,union(X1))
      | sP1(X1,X0) ),
    inference(resolution,[],[f192,f234]) ).

fof(f234,plain,
    ! [X0] : sP2(X0,union(X0)),
    inference(equality_resolution,[],[f199]) ).

fof(f199,plain,
    ! [X0,X1] :
      ( sP2(X0,X1)
      | union(X0) != X1 ),
    inference(cnf_transformation,[],[f117]) ).

fof(f117,plain,
    ! [X0,X1] :
      ( ( union(X0) = X1
        | ~ sP2(X0,X1) )
      & ( sP2(X0,X1)
        | union(X0) != X1 ) ),
    inference(nnf_transformation,[],[f92]) ).

fof(f92,plain,
    ! [X0,X1] :
      ( union(X0) = X1
    <=> sP2(X0,X1) ),
    inference(definition_folding,[],[f12,f91,f90]) ).

fof(f91,plain,
    ! [X0,X1] :
      ( sP2(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
        <=> sP1(X0,X2) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

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

fof(f192,plain,
    ! [X3,X0,X1] :
      ( ~ sP2(X0,X1)
      | ~ in(X3,X1)
      | sP1(X0,X3) ),
    inference(cnf_transformation,[],[f112]) ).

fof(f112,plain,
    ! [X0,X1] :
      ( ( sP2(X0,X1)
        | ( ( ~ sP1(X0,sK8(X0,X1))
            | ~ in(sK8(X0,X1),X1) )
          & ( sP1(X0,sK8(X0,X1))
            | in(sK8(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | ~ sP1(X0,X3) )
            & ( sP1(X0,X3)
              | ~ in(X3,X1) ) )
        | ~ sP2(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f110,f111]) ).

fof(f111,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ sP1(X0,X2)
            | ~ in(X2,X1) )
          & ( sP1(X0,X2)
            | in(X2,X1) ) )
     => ( ( ~ sP1(X0,sK8(X0,X1))
          | ~ in(sK8(X0,X1),X1) )
        & ( sP1(X0,sK8(X0,X1))
          | in(sK8(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f110,plain,
    ! [X0,X1] :
      ( ( sP2(X0,X1)
        | ? [X2] :
            ( ( ~ sP1(X0,X2)
              | ~ in(X2,X1) )
            & ( sP1(X0,X2)
              | in(X2,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | ~ sP1(X0,X3) )
            & ( sP1(X0,X3)
              | ~ in(X3,X1) ) )
        | ~ sP2(X0,X1) ) ),
    inference(rectify,[],[f109]) ).

fof(f109,plain,
    ! [X0,X1] :
      ( ( sP2(X0,X1)
        | ? [X2] :
            ( ( ~ sP1(X0,X2)
              | ~ in(X2,X1) )
            & ( sP1(X0,X2)
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | ~ sP1(X0,X2) )
            & ( sP1(X0,X2)
              | ~ in(X2,X1) ) )
        | ~ sP2(X0,X1) ) ),
    inference(nnf_transformation,[],[f91]) ).

fof(f27433,plain,
    ~ epsilon_connected(union(sK3)),
    inference(unit_resulting_resolution,[],[f144,f27424,f166]) ).

fof(f166,plain,
    ! [X0] :
      ( ~ epsilon_connected(X0)
      | ordinal(X0)
      | ~ epsilon_transitive(X0) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f65,plain,
    ! [X0] :
      ( ordinal(X0)
      | ~ epsilon_connected(X0)
      | ~ epsilon_transitive(X0) ),
    inference(flattening,[],[f64]) ).

fof(f64,plain,
    ! [X0] :
      ( ordinal(X0)
      | ~ epsilon_connected(X0)
      | ~ epsilon_transitive(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] :
      ( ( epsilon_connected(X0)
        & epsilon_transitive(X0) )
     => ordinal(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_ordinal1) ).

fof(f27424,plain,
    epsilon_transitive(union(sK3)),
    inference(subsumption_resolution,[],[f27412,f171]) ).

fof(f171,plain,
    ! [X0] :
      ( ~ subset(sK4(X0),X0)
      | epsilon_transitive(X0) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f99,plain,
    ! [X0] :
      ( ( epsilon_transitive(X0)
        | ( ~ subset(sK4(X0),X0)
          & in(sK4(X0),X0) ) )
      & ( ! [X2] :
            ( subset(X2,X0)
            | ~ in(X2,X0) )
        | ~ epsilon_transitive(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f97,f98]) ).

fof(f98,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ subset(X1,X0)
          & in(X1,X0) )
     => ( ~ subset(sK4(X0),X0)
        & in(sK4(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f97,plain,
    ! [X0] :
      ( ( epsilon_transitive(X0)
        | ? [X1] :
            ( ~ subset(X1,X0)
            & in(X1,X0) ) )
      & ( ! [X2] :
            ( subset(X2,X0)
            | ~ in(X2,X0) )
        | ~ epsilon_transitive(X0) ) ),
    inference(rectify,[],[f96]) ).

fof(f96,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(f27412,plain,
    ( epsilon_transitive(union(sK3))
    | subset(sK4(union(sK3)),union(sK3)) ),
    inference(resolution,[],[f27400,f187]) ).

fof(f187,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | subset(X0,union(X1)) ),
    inference(cnf_transformation,[],[f76]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( subset(X0,union(X1))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f45]) ).

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

fof(f27400,plain,
    ( in(sK4(union(sK3)),sK3)
    | epsilon_transitive(union(sK3)) ),
    inference(subsumption_resolution,[],[f27399,f1099]) ).

fof(f1099,plain,
    ~ empty(sK3),
    inference(unit_resulting_resolution,[],[f1047,f204]) ).

fof(f204,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | ~ empty(X1) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f84,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f43]) ).

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

fof(f1047,plain,
    in(sK9(sK3,sK7(union(sK3))),sK3),
    inference(unit_resulting_resolution,[],[f929,f197]) ).

fof(f197,plain,
    ! [X0,X1] :
      ( ~ sP1(X0,X1)
      | in(sK9(X0,X1),X0) ),
    inference(cnf_transformation,[],[f116]) ).

fof(f929,plain,
    sP1(sK3,sK7(union(sK3))),
    inference(unit_resulting_resolution,[],[f518,f234,f192]) ).

fof(f518,plain,
    in(sK7(union(sK3)),union(sK3)),
    inference(unit_resulting_resolution,[],[f262,f181,f184]) ).

fof(f184,plain,
    ! [X0,X1] :
      ( ~ element(X0,X1)
      | empty(X1)
      | in(X0,X1) ),
    inference(cnf_transformation,[],[f73]) ).

fof(f73,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(flattening,[],[f72]) ).

fof(f72,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(f181,plain,
    ! [X0] : element(sK7(X0),X0),
    inference(cnf_transformation,[],[f107]) ).

fof(f107,plain,
    ! [X0] : element(sK7(X0),X0),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f13,f106]) ).

fof(f106,plain,
    ! [X0] :
      ( ? [X1] : element(X1,X0)
     => element(sK7(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(f262,plain,
    ~ empty(union(sK3)),
    inference(unit_resulting_resolution,[],[f261,f165]) ).

fof(f165,plain,
    ! [X0] :
      ( ~ empty(X0)
      | sP0(X0) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f89,plain,
    ! [X0] :
      ( sP0(X0)
      | ~ empty(X0) ),
    inference(definition_folding,[],[f63,f88]) ).

fof(f88,plain,
    ! [X0] :
      ( ( ordinal(X0)
        & epsilon_connected(X0)
        & epsilon_transitive(X0) )
      | ~ sP0(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f63,plain,
    ! [X0] :
      ( ( ordinal(X0)
        & epsilon_connected(X0)
        & epsilon_transitive(X0) )
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0] :
      ( empty(X0)
     => ( ordinal(X0)
        & epsilon_connected(X0)
        & epsilon_transitive(X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_ordinal1) ).

fof(f261,plain,
    ~ sP0(union(sK3)),
    inference(unit_resulting_resolution,[],[f144,f164]) ).

fof(f164,plain,
    ! [X0] :
      ( ~ sP0(X0)
      | ordinal(X0) ),
    inference(cnf_transformation,[],[f95]) ).

fof(f95,plain,
    ! [X0] :
      ( ( ordinal(X0)
        & epsilon_connected(X0)
        & epsilon_transitive(X0) )
      | ~ sP0(X0) ),
    inference(nnf_transformation,[],[f88]) ).

fof(f27399,plain,
    ( epsilon_transitive(union(sK3))
    | empty(sK3)
    | in(sK4(union(sK3)),sK3) ),
    inference(resolution,[],[f27392,f184]) ).

fof(f27392,plain,
    ( element(sK4(union(sK3)),sK3)
    | epsilon_transitive(union(sK3)) ),
    inference(duplicate_literal_removal,[],[f27356]) ).

fof(f27356,plain,
    ( element(sK4(union(sK3)),sK3)
    | epsilon_transitive(union(sK3))
    | epsilon_transitive(union(sK3)) ),
    inference(resolution,[],[f27348,f1247]) ).

fof(f1247,plain,
    ! [X0] :
      ( in(sK4(union(X0)),sK9(X0,sK4(union(X0))))
      | epsilon_transitive(union(X0)) ),
    inference(resolution,[],[f1221,f196]) ).

fof(f1221,plain,
    ! [X0] :
      ( sP1(X0,sK4(union(X0)))
      | epsilon_transitive(union(X0)) ),
    inference(resolution,[],[f930,f170]) ).

fof(f170,plain,
    ! [X0] :
      ( in(sK4(X0),X0)
      | epsilon_transitive(X0) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f27348,plain,
    ! [X0] :
      ( ~ in(X0,sK9(sK3,sK4(union(sK3))))
      | element(X0,sK3)
      | epsilon_transitive(union(sK3)) ),
    inference(resolution,[],[f27346,f205]) ).

fof(f205,plain,
    ! [X2,X0,X1] :
      ( ~ element(X1,powerset(X2))
      | element(X0,X2)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f86]) ).

fof(f86,plain,
    ! [X0,X1,X2] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(flattening,[],[f85]) ).

fof(f85,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(f27346,plain,
    ( element(sK9(sK3,sK4(union(sK3))),powerset(sK3))
    | epsilon_transitive(union(sK3)) ),
    inference(resolution,[],[f27216,f202]) ).

fof(f202,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | element(X0,powerset(X1)) ),
    inference(cnf_transformation,[],[f118]) ).

fof(f118,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(f27216,plain,
    ( subset(sK9(sK3,sK4(union(sK3))),sK3)
    | epsilon_transitive(union(sK3)) ),
    inference(resolution,[],[f4108,f246]) ).

fof(f246,plain,
    epsilon_transitive(sK3),
    inference(unit_resulting_resolution,[],[f143,f156]) ).

fof(f156,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(f143,plain,
    ordinal(sK3),
    inference(cnf_transformation,[],[f94]) ).

fof(f94,plain,
    ( ~ ordinal(union(sK3))
    & ordinal(sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f56,f93]) ).

fof(f93,plain,
    ( ? [X0] :
        ( ~ ordinal(union(X0))
        & ordinal(X0) )
   => ( ~ ordinal(union(sK3))
      & ordinal(sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f56,plain,
    ? [X0] :
      ( ~ ordinal(union(X0))
      & ordinal(X0) ),
    inference(ennf_transformation,[],[f38]) ).

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

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

fof(f4108,plain,
    ! [X0] :
      ( ~ epsilon_transitive(X0)
      | subset(sK9(X0,sK4(union(X0))),X0)
      | epsilon_transitive(union(X0)) ),
    inference(resolution,[],[f1246,f169]) ).

fof(f169,plain,
    ! [X2,X0] :
      ( ~ in(X2,X0)
      | subset(X2,X0)
      | ~ epsilon_transitive(X0) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f1246,plain,
    ! [X0] :
      ( in(sK9(X0,sK4(union(X0))),X0)
      | epsilon_transitive(union(X0)) ),
    inference(resolution,[],[f1221,f197]) ).

fof(f144,plain,
    ~ ordinal(union(sK3)),
    inference(cnf_transformation,[],[f94]) ).

fof(f28290,plain,
    ~ in(sK6(union(sK3)),sK9(sK3,sK6(union(sK3)))),
    inference(unit_resulting_resolution,[],[f27432,f28231,f183]) ).

fof(f183,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | ordinal(X0)
      | ~ ordinal(X1) ),
    inference(cnf_transformation,[],[f71]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( ordinal(X0)
      | ~ in(X0,X1)
      | ~ ordinal(X1) ),
    inference(flattening,[],[f70]) ).

fof(f70,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(f28231,plain,
    ~ ordinal(sK6(union(sK3))),
    inference(unit_resulting_resolution,[],[f27493,f27495,f27494,f28194,f158]) ).

fof(f158,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(f28194,plain,
    ordinal(sK5(union(sK3))),
    inference(unit_resulting_resolution,[],[f27431,f27468,f183]) ).

fof(f27468,plain,
    in(sK5(union(sK3)),sK9(sK3,sK5(union(sK3)))),
    inference(unit_resulting_resolution,[],[f27433,f1257]) ).

fof(f1257,plain,
    ! [X0] :
      ( in(sK5(union(X0)),sK9(X0,sK5(union(X0))))
      | epsilon_connected(union(X0)) ),
    inference(resolution,[],[f1222,f196]) ).

fof(f1222,plain,
    ! [X0] :
      ( sP1(X0,sK5(union(X0)))
      | epsilon_connected(union(X0)) ),
    inference(resolution,[],[f930,f173]) ).

fof(f173,plain,
    ! [X0] :
      ( in(sK5(X0),X0)
      | epsilon_connected(X0) ),
    inference(cnf_transformation,[],[f103]) ).

fof(f27431,plain,
    ordinal(sK9(sK3,sK5(union(sK3)))),
    inference(unit_resulting_resolution,[],[f27424,f13739]) ).

fof(f13739,plain,
    ( ~ epsilon_transitive(union(sK3))
    | ordinal(sK9(sK3,sK5(union(sK3)))) ),
    inference(subsumption_resolution,[],[f13738,f144]) ).

fof(f13738,plain,
    ( ordinal(sK9(sK3,sK5(union(sK3))))
    | ordinal(union(sK3))
    | ~ epsilon_transitive(union(sK3)) ),
    inference(resolution,[],[f13648,f166]) ).

fof(f13648,plain,
    ( epsilon_connected(union(sK3))
    | ordinal(sK9(sK3,sK5(union(sK3)))) ),
    inference(resolution,[],[f4224,f143]) ).

fof(f4224,plain,
    ! [X0] :
      ( ~ ordinal(X0)
      | ordinal(sK9(X0,sK5(union(X0))))
      | epsilon_connected(union(X0)) ),
    inference(resolution,[],[f1256,f183]) ).

fof(f1256,plain,
    ! [X0] :
      ( in(sK9(X0,sK5(union(X0))),X0)
      | epsilon_connected(union(X0)) ),
    inference(resolution,[],[f1222,f197]) ).

fof(f27494,plain,
    sK5(union(sK3)) != sK6(union(sK3)),
    inference(unit_resulting_resolution,[],[f27433,f176]) ).

fof(f176,plain,
    ! [X0] :
      ( sK5(X0) != sK6(X0)
      | epsilon_connected(X0) ),
    inference(cnf_transformation,[],[f103]) ).

fof(f27495,plain,
    ~ in(sK6(union(sK3)),sK5(union(sK3))),
    inference(unit_resulting_resolution,[],[f27433,f177]) ).

fof(f177,plain,
    ! [X0] :
      ( ~ in(sK6(X0),sK5(X0))
      | epsilon_connected(X0) ),
    inference(cnf_transformation,[],[f103]) ).

fof(f27493,plain,
    ~ in(sK5(union(sK3)),sK6(union(sK3))),
    inference(unit_resulting_resolution,[],[f27433,f175]) ).

fof(f175,plain,
    ! [X0] :
      ( ~ in(sK5(X0),sK6(X0))
      | epsilon_connected(X0) ),
    inference(cnf_transformation,[],[f103]) ).

fof(f27432,plain,
    ordinal(sK9(sK3,sK6(union(sK3)))),
    inference(unit_resulting_resolution,[],[f27424,f13878]) ).

fof(f13878,plain,
    ( ~ epsilon_transitive(union(sK3))
    | ordinal(sK9(sK3,sK6(union(sK3)))) ),
    inference(subsumption_resolution,[],[f13877,f144]) ).

fof(f13877,plain,
    ( ordinal(sK9(sK3,sK6(union(sK3))))
    | ordinal(union(sK3))
    | ~ epsilon_transitive(union(sK3)) ),
    inference(resolution,[],[f13786,f166]) ).

fof(f13786,plain,
    ( epsilon_connected(union(sK3))
    | ordinal(sK9(sK3,sK6(union(sK3)))) ),
    inference(resolution,[],[f4346,f143]) ).

fof(f4346,plain,
    ! [X0] :
      ( ~ ordinal(X0)
      | ordinal(sK9(X0,sK6(union(X0))))
      | epsilon_connected(union(X0)) ),
    inference(resolution,[],[f1266,f183]) ).

fof(f1266,plain,
    ! [X0] :
      ( in(sK9(X0,sK6(union(X0))),X0)
      | epsilon_connected(union(X0)) ),
    inference(resolution,[],[f1223,f197]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : NUM397+1 : TPTP v8.2.0. Released v3.2.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36  % Computer : n023.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Mon May 20 04:15:08 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  % (19824)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.38  % (19827)WARNING: value z3 for option sas not known
% 0.21/0.38  % (19825)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.38  % (19826)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.38  % (19828)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.38  % (19827)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)
% 0.21/0.38  % (19829)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)
% 0.21/0.38  % (19830)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)
% 0.21/0.38  % (19831)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)
% 0.21/0.38  TRYING [1]
% 0.21/0.38  TRYING [2]
% 0.21/0.39  TRYING [3]
% 0.21/0.39  TRYING [1]
% 0.21/0.39  TRYING [4]
% 0.21/0.39  TRYING [2]
% 0.21/0.40  TRYING [3]
% 0.21/0.40  TRYING [5]
% 0.21/0.42  TRYING [6]
% 0.21/0.43  TRYING [4]
% 0.21/0.46  TRYING [7]
% 0.21/0.49  TRYING [5]
% 1.26/0.54  TRYING [8]
% 1.99/0.64  TRYING [6]
% 3.51/0.88  TRYING [1]
% 3.51/0.88  TRYING [2]
% 3.51/0.88  TRYING [3]
% 3.51/0.89  TRYING [4]
% 3.51/0.90  TRYING [5]
% 3.51/0.92  TRYING [6]
% 4.08/0.95  TRYING [7]
% 4.43/1.00  TRYING [9]
% 4.43/1.04  % (19831)First to succeed.
% 4.43/1.04  % (19831)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-19824"
% 4.43/1.05  % (19831)Refutation found. Thanks to Tanya!
% 4.43/1.05  % SZS status Theorem for theBenchmark
% 4.43/1.05  % SZS output start Proof for theBenchmark
% See solution above
% 4.43/1.05  % (19831)------------------------------
% 4.43/1.05  % (19831)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 4.43/1.05  % (19831)Termination reason: Refutation
% 4.43/1.05  
% 4.43/1.05  % (19831)Memory used [KB]: 8836
% 4.43/1.05  % (19831)Time elapsed: 0.664 s
% 4.43/1.05  % (19831)Instructions burned: 1714 (million)
% 4.43/1.05  % (19824)Success in time 0.672 s
%------------------------------------------------------------------------------