TSTP Solution File: SET810+4 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET810+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n020.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 : Wed Aug 31 18:22:20 EDT 2022

% Result   : Theorem 0.22s 0.55s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   75 (  12 unt;   0 def)
%            Number of atoms       :  367 (   0 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  440 ( 148   ~; 127   |; 124   &)
%                                         (  19 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   10 (   9 usr;   2 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   4 con; 0-2 aty)
%            Number of variables   :  205 ( 162   !;  43   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f455,plain,
    $false,
    inference(avatar_sat_refutation,[],[f431,f454]) ).

fof(f454,plain,
    spl15_10,
    inference(avatar_contradiction_clause,[],[f453]) ).

fof(f453,plain,
    ( $false
    | spl15_10 ),
    inference(subsumption_resolution,[],[f450,f143]) ).

fof(f143,plain,
    strict_well_order(member_predicate,sK12),
    inference(resolution,[],[f107,f79]) ).

fof(f79,plain,
    ! [X0] :
      ( ~ member(X0,on)
      | strict_well_order(member_predicate,X0) ),
    inference(cnf_transformation,[],[f47]) ).

fof(f47,plain,
    ! [X0] :
      ( ( member(X0,on)
        | ~ set(X0)
        | ~ strict_well_order(member_predicate,X0)
        | ( member(sK1(X0),X0)
          & ~ subset(sK1(X0),X0) ) )
      & ( ( set(X0)
          & strict_well_order(member_predicate,X0)
          & ! [X2] :
              ( ~ member(X2,X0)
              | subset(X2,X0) ) )
        | ~ member(X0,on) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f45,f46]) ).

fof(f46,plain,
    ! [X0] :
      ( ? [X1] :
          ( member(X1,X0)
          & ~ subset(X1,X0) )
     => ( member(sK1(X0),X0)
        & ~ subset(sK1(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f45,plain,
    ! [X0] :
      ( ( member(X0,on)
        | ~ set(X0)
        | ~ strict_well_order(member_predicate,X0)
        | ? [X1] :
            ( member(X1,X0)
            & ~ subset(X1,X0) ) )
      & ( ( set(X0)
          & strict_well_order(member_predicate,X0)
          & ! [X2] :
              ( ~ member(X2,X0)
              | subset(X2,X0) ) )
        | ~ member(X0,on) ) ),
    inference(rectify,[],[f44]) ).

fof(f44,plain,
    ! [X0] :
      ( ( member(X0,on)
        | ~ set(X0)
        | ~ strict_well_order(member_predicate,X0)
        | ? [X1] :
            ( member(X1,X0)
            & ~ subset(X1,X0) ) )
      & ( ( set(X0)
          & strict_well_order(member_predicate,X0)
          & ! [X1] :
              ( ~ member(X1,X0)
              | subset(X1,X0) ) )
        | ~ member(X0,on) ) ),
    inference(flattening,[],[f43]) ).

fof(f43,plain,
    ! [X0] :
      ( ( member(X0,on)
        | ~ set(X0)
        | ~ strict_well_order(member_predicate,X0)
        | ? [X1] :
            ( member(X1,X0)
            & ~ subset(X1,X0) ) )
      & ( ( set(X0)
          & strict_well_order(member_predicate,X0)
          & ! [X1] :
              ( ~ member(X1,X0)
              | subset(X1,X0) ) )
        | ~ member(X0,on) ) ),
    inference(nnf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0] :
      ( member(X0,on)
    <=> ( set(X0)
        & strict_well_order(member_predicate,X0)
        & ! [X1] :
            ( ~ member(X1,X0)
            | subset(X1,X0) ) ) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0] :
      ( ( set(X0)
        & ! [X1] :
            ( member(X1,X0)
           => subset(X1,X0) )
        & strict_well_order(member_predicate,X0) )
    <=> member(X0,on) ),
    inference(rectify,[],[f12]) ).

fof(f12,axiom,
    ! [X0] :
      ( member(X0,on)
    <=> ( ! [X2] :
            ( member(X2,X0)
           => subset(X2,X0) )
        & strict_well_order(member_predicate,X0)
        & set(X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinal_number) ).

fof(f107,plain,
    member(sK12,on),
    inference(cnf_transformation,[],[f71]) ).

fof(f71,plain,
    ( member(sK11,on)
    & member(sK12,sK11)
    & member(sK12,on)
    & member(sK11,sK12) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12])],[f69,f70]) ).

fof(f70,plain,
    ( ? [X0,X1] :
        ( member(X0,on)
        & member(X1,X0)
        & member(X1,on)
        & member(X0,X1) )
   => ( member(sK11,on)
      & member(sK12,sK11)
      & member(sK12,on)
      & member(sK11,sK12) ) ),
    introduced(choice_axiom,[]) ).

fof(f69,plain,
    ? [X0,X1] :
      ( member(X0,on)
      & member(X1,X0)
      & member(X1,on)
      & member(X0,X1) ),
    inference(rectify,[],[f33]) ).

fof(f33,plain,
    ? [X1,X0] :
      ( member(X1,on)
      & member(X0,X1)
      & member(X0,on)
      & member(X1,X0) ),
    inference(flattening,[],[f32]) ).

fof(f32,plain,
    ? [X1,X0] :
      ( member(X1,X0)
      & member(X0,X1)
      & member(X0,on)
      & member(X1,on) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,plain,
    ~ ! [X1,X0] :
        ( ( member(X0,on)
          & member(X1,on) )
       => ~ ( member(X1,X0)
            & member(X0,X1) ) ),
    inference(rectify,[],[f21]) ).

fof(f21,negated_conjecture,
    ~ ! [X1,X0] :
        ( ( member(X1,on)
          & member(X0,on) )
       => ~ ( member(X1,X0)
            & member(X0,X1) ) ),
    inference(negated_conjecture,[],[f20]) ).

fof(f20,conjecture,
    ! [X1,X0] :
      ( ( member(X1,on)
        & member(X0,on) )
     => ~ ( member(X1,X0)
          & member(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thV3) ).

fof(f450,plain,
    ( ~ strict_well_order(member_predicate,sK12)
    | spl15_10 ),
    inference(resolution,[],[f424,f105]) ).

fof(f105,plain,
    ! [X0,X1] :
      ( ~ strict_well_order(X0,X1)
      | strict_order(X0,X1) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( ( ( strict_order(X0,X1)
          & ! [X2] :
              ( ! [X3] : ~ member(X3,X2)
              | least(sK8(X0,X2),X0,X2)
              | ~ subset(X2,X1) ) )
        | ~ strict_well_order(X0,X1) )
      & ( strict_well_order(X0,X1)
        | ~ strict_order(X0,X1)
        | ( member(sK10(X0,X1),sK9(X0,X1))
          & ! [X7] : ~ least(X7,X0,sK9(X0,X1))
          & subset(sK9(X0,X1),X1) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f64,f67,f66,f65]) ).

fof(f65,plain,
    ! [X0,X2] :
      ( ? [X4] : least(X4,X0,X2)
     => least(sK8(X0,X2),X0,X2) ),
    introduced(choice_axiom,[]) ).

fof(f66,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( ? [X6] : member(X6,X5)
          & ! [X7] : ~ least(X7,X0,X5)
          & subset(X5,X1) )
     => ( ? [X6] : member(X6,sK9(X0,X1))
        & ! [X7] : ~ least(X7,X0,sK9(X0,X1))
        & subset(sK9(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f67,plain,
    ! [X0,X1] :
      ( ? [X6] : member(X6,sK9(X0,X1))
     => member(sK10(X0,X1),sK9(X0,X1)) ),
    introduced(choice_axiom,[]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( ( ( strict_order(X0,X1)
          & ! [X2] :
              ( ! [X3] : ~ member(X3,X2)
              | ? [X4] : least(X4,X0,X2)
              | ~ subset(X2,X1) ) )
        | ~ strict_well_order(X0,X1) )
      & ( strict_well_order(X0,X1)
        | ~ strict_order(X0,X1)
        | ? [X5] :
            ( ? [X6] : member(X6,X5)
            & ! [X7] : ~ least(X7,X0,X5)
            & subset(X5,X1) ) ) ),
    inference(rectify,[],[f63]) ).

fof(f63,plain,
    ! [X1,X0] :
      ( ( ( strict_order(X1,X0)
          & ! [X2] :
              ( ! [X3] : ~ member(X3,X2)
              | ? [X4] : least(X4,X1,X2)
              | ~ subset(X2,X0) ) )
        | ~ strict_well_order(X1,X0) )
      & ( strict_well_order(X1,X0)
        | ~ strict_order(X1,X0)
        | ? [X2] :
            ( ? [X3] : member(X3,X2)
            & ! [X4] : ~ least(X4,X1,X2)
            & subset(X2,X0) ) ) ),
    inference(flattening,[],[f62]) ).

fof(f62,plain,
    ! [X1,X0] :
      ( ( ( strict_order(X1,X0)
          & ! [X2] :
              ( ! [X3] : ~ member(X3,X2)
              | ? [X4] : least(X4,X1,X2)
              | ~ subset(X2,X0) ) )
        | ~ strict_well_order(X1,X0) )
      & ( strict_well_order(X1,X0)
        | ~ strict_order(X1,X0)
        | ? [X2] :
            ( ? [X3] : member(X3,X2)
            & ! [X4] : ~ least(X4,X1,X2)
            & subset(X2,X0) ) ) ),
    inference(nnf_transformation,[],[f31]) ).

fof(f31,plain,
    ! [X1,X0] :
      ( ( strict_order(X1,X0)
        & ! [X2] :
            ( ! [X3] : ~ member(X3,X2)
            | ? [X4] : least(X4,X1,X2)
            | ~ subset(X2,X0) ) )
    <=> strict_well_order(X1,X0) ),
    inference(flattening,[],[f30]) ).

fof(f30,plain,
    ! [X1,X0] :
      ( ( strict_order(X1,X0)
        & ! [X2] :
            ( ? [X4] : least(X4,X1,X2)
            | ! [X3] : ~ member(X3,X2)
            | ~ subset(X2,X0) ) )
    <=> strict_well_order(X1,X0) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X1,X0] :
      ( ( strict_order(X1,X0)
        & ! [X2] :
            ( ( ? [X3] : member(X3,X2)
              & subset(X2,X0) )
           => ? [X4] : least(X4,X1,X2) ) )
    <=> strict_well_order(X1,X0) ),
    inference(rectify,[],[f13]) ).

fof(f13,axiom,
    ! [X3,X5] :
      ( ( ! [X0] :
            ( ( ? [X2] : member(X2,X0)
              & subset(X0,X3) )
           => ? [X4] : least(X4,X5,X0) )
        & strict_order(X5,X3) )
    <=> strict_well_order(X5,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',strict_well_order) ).

fof(f424,plain,
    ( ~ strict_order(member_predicate,sK12)
    | spl15_10 ),
    inference(avatar_component_clause,[],[f422]) ).

fof(f422,plain,
    ( spl15_10
  <=> strict_order(member_predicate,sK12) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_10])]) ).

fof(f431,plain,
    ~ spl15_10,
    inference(avatar_split_clause,[],[f430,f422]) ).

fof(f430,plain,
    ~ strict_order(member_predicate,sK12),
    inference(subsumption_resolution,[],[f429,f314]) ).

fof(f314,plain,
    member(sK12,sK12),
    inference(resolution,[],[f278,f185]) ).

fof(f185,plain,
    ! [X0] :
      ( ~ subset(sK11,X0)
      | member(sK12,X0) ),
    inference(resolution,[],[f108,f85]) ).

fof(f85,plain,
    ! [X2,X0,X1] :
      ( ~ subset(X0,X1)
      | member(X2,X1)
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f51]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( member(X2,X1)
            | ~ member(X2,X0) )
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ( ~ member(sK2(X0,X1),X1)
          & member(sK2(X0,X1),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f49,f50]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ~ member(X3,X1)
          & member(X3,X0) )
     => ( ~ member(sK2(X0,X1),X1)
        & member(sK2(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( member(X2,X1)
            | ~ member(X2,X0) )
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ? [X3] :
            ( ~ member(X3,X1)
            & member(X3,X0) ) ) ),
    inference(rectify,[],[f48]) ).

fof(f48,plain,
    ! [X1,X0] :
      ( ( ! [X2] :
            ( member(X2,X0)
            | ~ member(X2,X1) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ? [X2] :
            ( ~ member(X2,X0)
            & member(X2,X1) ) ) ),
    inference(nnf_transformation,[],[f40]) ).

fof(f40,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( member(X2,X0)
          | ~ member(X2,X1) )
    <=> subset(X1,X0) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X1,X0] :
      ( subset(X1,X0)
    <=> ! [X2] :
          ( member(X2,X1)
         => member(X2,X0) ) ),
    inference(rectify,[],[f1]) ).

fof(f1,axiom,
    ! [X1,X0] :
      ( ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) )
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).

fof(f108,plain,
    member(sK12,sK11),
    inference(cnf_transformation,[],[f71]) ).

fof(f278,plain,
    subset(sK11,sK12),
    inference(resolution,[],[f142,f106]) ).

fof(f106,plain,
    member(sK11,sK12),
    inference(cnf_transformation,[],[f71]) ).

fof(f142,plain,
    ! [X0] :
      ( ~ member(X0,sK12)
      | subset(X0,sK12) ),
    inference(resolution,[],[f107,f78]) ).

fof(f78,plain,
    ! [X2,X0] :
      ( ~ member(X2,X0)
      | ~ member(X0,on)
      | subset(X2,X0) ),
    inference(cnf_transformation,[],[f47]) ).

fof(f429,plain,
    ( ~ strict_order(member_predicate,sK12)
    | ~ member(sK12,sK12) ),
    inference(subsumption_resolution,[],[f407,f191]) ).

fof(f191,plain,
    apply(member_predicate,sK12,sK11),
    inference(resolution,[],[f108,f99]) ).

fof(f99,plain,
    ! [X0,X1] :
      ( apply(member_predicate,X1,X0)
      | ~ member(X1,X0) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( ( member(X1,X0)
        | ~ apply(member_predicate,X1,X0) )
      & ( apply(member_predicate,X1,X0)
        | ~ member(X1,X0) ) ),
    inference(nnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( member(X1,X0)
    <=> apply(member_predicate,X1,X0) ),
    inference(rectify,[],[f15]) ).

fof(f15,axiom,
    ! [X4,X2] :
      ( member(X2,X4)
    <=> apply(member_predicate,X2,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rel_member) ).

fof(f407,plain,
    ( ~ strict_order(member_predicate,sK12)
    | ~ apply(member_predicate,sK12,sK11)
    | ~ member(sK12,sK12) ),
    inference(resolution,[],[f125,f127]) ).

fof(f127,plain,
    apply(member_predicate,sK11,sK12),
    inference(resolution,[],[f106,f99]) ).

fof(f125,plain,
    ! [X10,X11] :
      ( ~ apply(X10,sK11,X11)
      | ~ apply(X10,X11,sK11)
      | ~ strict_order(X10,sK12)
      | ~ member(X11,sK12) ),
    inference(resolution,[],[f106,f93]) ).

fof(f93,plain,
    ! [X0,X1,X4,X5] :
      ( ~ member(X5,X1)
      | ~ apply(X0,X4,X5)
      | ~ strict_order(X0,X1)
      | ~ apply(X0,X5,X4)
      | ~ member(X4,X1) ),
    inference(cnf_transformation,[],[f60]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( ( strict_order(X0,X1)
        | ~ sP0(X1,X0)
        | ( apply(X0,sK7(X0,X1),sK6(X0,X1))
          & member(sK6(X0,X1),X1)
          & member(sK7(X0,X1),X1)
          & apply(X0,sK6(X0,X1),sK7(X0,X1)) ) )
      & ( ( sP0(X1,X0)
          & ! [X4,X5] :
              ( ~ apply(X0,X5,X4)
              | ~ member(X4,X1)
              | ~ member(X5,X1)
              | ~ apply(X0,X4,X5) ) )
        | ~ strict_order(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f58,f59]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( ? [X2,X3] :
          ( apply(X0,X3,X2)
          & member(X2,X1)
          & member(X3,X1)
          & apply(X0,X2,X3) )
     => ( apply(X0,sK7(X0,X1),sK6(X0,X1))
        & member(sK6(X0,X1),X1)
        & member(sK7(X0,X1),X1)
        & apply(X0,sK6(X0,X1),sK7(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( ( strict_order(X0,X1)
        | ~ sP0(X1,X0)
        | ? [X2,X3] :
            ( apply(X0,X3,X2)
            & member(X2,X1)
            & member(X3,X1)
            & apply(X0,X2,X3) ) )
      & ( ( sP0(X1,X0)
          & ! [X4,X5] :
              ( ~ apply(X0,X5,X4)
              | ~ member(X4,X1)
              | ~ member(X5,X1)
              | ~ apply(X0,X4,X5) ) )
        | ~ strict_order(X0,X1) ) ),
    inference(rectify,[],[f57]) ).

fof(f57,plain,
    ! [X1,X0] :
      ( ( strict_order(X1,X0)
        | ~ sP0(X0,X1)
        | ? [X2,X3] :
            ( apply(X1,X3,X2)
            & member(X2,X0)
            & member(X3,X0)
            & apply(X1,X2,X3) ) )
      & ( ( sP0(X0,X1)
          & ! [X2,X3] :
              ( ~ apply(X1,X3,X2)
              | ~ member(X2,X0)
              | ~ member(X3,X0)
              | ~ apply(X1,X2,X3) ) )
        | ~ strict_order(X1,X0) ) ),
    inference(flattening,[],[f56]) ).

fof(f56,plain,
    ! [X1,X0] :
      ( ( strict_order(X1,X0)
        | ~ sP0(X0,X1)
        | ? [X2,X3] :
            ( apply(X1,X3,X2)
            & member(X2,X0)
            & member(X3,X0)
            & apply(X1,X2,X3) ) )
      & ( ( sP0(X0,X1)
          & ! [X2,X3] :
              ( ~ apply(X1,X3,X2)
              | ~ member(X2,X0)
              | ~ member(X3,X0)
              | ~ apply(X1,X2,X3) ) )
        | ~ strict_order(X1,X0) ) ),
    inference(nnf_transformation,[],[f42]) ).

fof(f42,plain,
    ! [X1,X0] :
      ( strict_order(X1,X0)
    <=> ( sP0(X0,X1)
        & ! [X2,X3] :
            ( ~ apply(X1,X3,X2)
            | ~ member(X2,X0)
            | ~ member(X3,X0)
            | ~ apply(X1,X2,X3) ) ) ),
    inference(definition_folding,[],[f35,f41]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
    <=> ! [X5,X4,X6] :
          ( ~ member(X5,X0)
          | ~ member(X6,X0)
          | apply(X1,X5,X4)
          | ~ member(X4,X0)
          | ~ apply(X1,X5,X6)
          | ~ apply(X1,X6,X4) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f35,plain,
    ! [X1,X0] :
      ( strict_order(X1,X0)
    <=> ( ! [X5,X4,X6] :
            ( ~ member(X5,X0)
            | ~ member(X6,X0)
            | apply(X1,X5,X4)
            | ~ member(X4,X0)
            | ~ apply(X1,X5,X6)
            | ~ apply(X1,X6,X4) )
        & ! [X2,X3] :
            ( ~ apply(X1,X3,X2)
            | ~ member(X2,X0)
            | ~ member(X3,X0)
            | ~ apply(X1,X2,X3) ) ) ),
    inference(flattening,[],[f34]) ).

fof(f34,plain,
    ! [X1,X0] :
      ( ( ! [X6,X5,X4] :
            ( apply(X1,X5,X4)
            | ~ apply(X1,X6,X4)
            | ~ apply(X1,X5,X6)
            | ~ member(X4,X0)
            | ~ member(X5,X0)
            | ~ member(X6,X0) )
        & ! [X3,X2] :
            ( ~ apply(X1,X2,X3)
            | ~ apply(X1,X3,X2)
            | ~ member(X2,X0)
            | ~ member(X3,X0) ) )
    <=> strict_order(X1,X0) ),
    inference(ennf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X1,X0] :
      ( ( ! [X6,X5,X4] :
            ( ( member(X4,X0)
              & member(X5,X0)
              & member(X6,X0) )
           => ( ( apply(X1,X6,X4)
                & apply(X1,X5,X6) )
             => apply(X1,X5,X4) ) )
        & ! [X3,X2] :
            ( ( member(X2,X0)
              & member(X3,X0) )
           => ~ ( apply(X1,X2,X3)
                & apply(X1,X3,X2) ) ) )
    <=> strict_order(X1,X0) ),
    inference(rectify,[],[f16]) ).

fof(f16,axiom,
    ! [X3,X5] :
      ( strict_order(X5,X3)
    <=> ( ! [X2,X4] :
            ( ( member(X2,X3)
              & member(X4,X3) )
           => ~ ( apply(X5,X2,X4)
                & apply(X5,X4,X2) ) )
        & ! [X7,X2,X4] :
            ( ( member(X4,X3)
              & member(X7,X3)
              & member(X2,X3) )
           => ( ( apply(X5,X2,X4)
                & apply(X5,X4,X7) )
             => apply(X5,X2,X7) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',strict_order) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : SET810+4 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.14/0.35  % Computer : n020.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   : Tue Aug 30 14:23:15 EDT 2022
% 0.14/0.35  % CPUTime    : 
% 0.22/0.50  % (22373)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.50  % (22381)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.22/0.51  % (22373)Instruction limit reached!
% 0.22/0.51  % (22373)------------------------------
% 0.22/0.51  % (22373)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.22/0.51  % (22373)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.22/0.51  % (22373)Termination reason: Unknown
% 0.22/0.51  % (22373)Termination phase: Saturation
% 0.22/0.51  
% 0.22/0.51  % (22373)Memory used [KB]: 1535
% 0.22/0.51  % (22373)Time elapsed: 0.005 s
% 0.22/0.51  % (22373)Instructions burned: 3 (million)
% 0.22/0.51  % (22373)------------------------------
% 0.22/0.51  % (22373)------------------------------
% 0.22/0.51  % (22365)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.22/0.52  % (22361)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.52  % (22362)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.22/0.53  % (22362)Refutation not found, incomplete strategy% (22362)------------------------------
% 0.22/0.53  % (22362)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.22/0.53  % (22385)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.22/0.53  % (22362)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.22/0.53  % (22362)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.53  
% 0.22/0.53  % (22362)Memory used [KB]: 5884
% 0.22/0.53  % (22362)Time elapsed: 0.119 s
% 0.22/0.53  % (22382)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.22/0.53  % (22362)------------------------------
% 0.22/0.53  % (22362)------------------------------
% 0.22/0.53  % (22364)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.22/0.53  % (22383)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.22/0.53  % (22377)ott+1010_1:1_sd=2:sos=on:sp=occurrence:ss=axioms:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.22/0.53  % (22359)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.22/0.53  % (22386)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 0.22/0.53  % (22377)Instruction limit reached!
% 0.22/0.53  % (22377)------------------------------
% 0.22/0.53  % (22377)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.22/0.53  % (22363)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.22/0.53  % (22360)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.22/0.53  % (22388)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 0.22/0.53  % (22376)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.54  % (22364)Refutation not found, incomplete strategy% (22364)------------------------------
% 0.22/0.54  % (22364)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.22/0.54  % (22385)Refutation not found, incomplete strategy% (22385)------------------------------
% 0.22/0.54  % (22385)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.22/0.54  % (22377)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.22/0.54  % (22377)Termination reason: Unknown
% 0.22/0.54  % (22377)Termination phase: Saturation
% 0.22/0.54  
% 0.22/0.54  % (22377)Memory used [KB]: 1407
% 0.22/0.54  % (22377)Time elapsed: 0.003 s
% 0.22/0.54  % (22377)Instructions burned: 2 (million)
% 0.22/0.54  % (22377)------------------------------
% 0.22/0.54  % (22377)------------------------------
% 0.22/0.54  % (22378)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 0.22/0.54  % (22369)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.22/0.54  % (22378)Refutation not found, incomplete strategy% (22378)------------------------------
% 0.22/0.54  % (22378)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.22/0.54  % (22380)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.22/0.54  % (22364)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.22/0.54  % (22364)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.54  
% 0.22/0.54  % (22364)Memory used [KB]: 1535
% 0.22/0.54  % (22364)Time elapsed: 0.127 s
% 0.22/0.54  % (22364)Instructions burned: 2 (million)
% 0.22/0.54  % (22364)------------------------------
% 0.22/0.54  % (22364)------------------------------
% 0.22/0.54  % (22384)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 0.22/0.54  % (22361)Instruction limit reached!
% 0.22/0.54  % (22361)------------------------------
% 0.22/0.54  % (22361)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.22/0.54  % (22361)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.22/0.54  % (22361)Termination reason: Unknown
% 0.22/0.54  % (22361)Termination phase: Property scanning
% 0.22/0.54  
% 0.22/0.54  % (22361)Memory used [KB]: 1535
% 0.22/0.54  % (22361)Time elapsed: 0.003 s
% 0.22/0.54  % (22361)Instructions burned: 3 (million)
% 0.22/0.54  % (22361)------------------------------
% 0.22/0.54  % (22361)------------------------------
% 0.22/0.54  % (22372)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.22/0.54  % (22360)Instruction limit reached!
% 0.22/0.54  % (22360)------------------------------
% 0.22/0.54  % (22360)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.22/0.54  % (22368)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.22/0.54  % (22369)First to succeed.
% 0.22/0.54  % (22385)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.22/0.54  % (22385)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.54  
% 0.22/0.54  % (22385)Memory used [KB]: 6140
% 0.22/0.54  % (22385)Time elapsed: 0.131 s
% 0.22/0.54  % (22385)Instructions burned: 5 (million)
% 0.22/0.54  % (22385)------------------------------
% 0.22/0.54  % (22385)------------------------------
% 0.22/0.54  % (22374)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.22/0.54  % (22375)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.22/0.54  % (22363)Instruction limit reached!
% 0.22/0.54  % (22363)------------------------------
% 0.22/0.54  % (22363)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.22/0.54  % (22367)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.22/0.54  % (22370)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.22/0.54  % (22366)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.22/0.55  % (22375)Refutation not found, incomplete strategy% (22375)------------------------------
% 0.22/0.55  % (22375)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.22/0.55  % (22371)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.22/0.55  % (22378)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.22/0.55  % (22378)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.55  
% 0.22/0.55  % (22378)Memory used [KB]: 5884
% 0.22/0.55  % (22378)Time elapsed: 0.132 s
% 0.22/0.55  % (22378)Instructions burned: 2 (million)
% 0.22/0.55  % (22378)------------------------------
% 0.22/0.55  % (22378)------------------------------
% 0.22/0.55  % (22374)Instruction limit reached!
% 0.22/0.55  % (22374)------------------------------
% 0.22/0.55  % (22374)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.22/0.55  % (22376)Instruction limit reached!
% 0.22/0.55  % (22376)------------------------------
% 0.22/0.55  % (22376)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.22/0.55  % (22369)Refutation found. Thanks to Tanya!
% 0.22/0.55  % SZS status Theorem for theBenchmark
% 0.22/0.55  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.55  % (22369)------------------------------
% 0.22/0.55  % (22369)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.22/0.55  % (22369)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.22/0.55  % (22369)Termination reason: Refutation
% 0.22/0.55  
% 0.22/0.55  % (22369)Memory used [KB]: 6140
% 0.22/0.55  % (22369)Time elapsed: 0.149 s
% 0.22/0.55  % (22369)Instructions burned: 9 (million)
% 0.22/0.55  % (22369)------------------------------
% 0.22/0.55  % (22369)------------------------------
% 0.22/0.55  % (22358)Success in time 0.191 s
%------------------------------------------------------------------------------