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

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---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_sat --cores 0 -t %d %s

% Computer : n021.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 18:25:42 EDT 2022

% Result   : Theorem 1.42s 0.59s
% Output   : Refutation 1.42s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   70 (  11 unt;   0 def)
%            Number of atoms       :  358 (   0 equ)
%            Maximal formula atoms :   12 (   5 avg)
%            Number of connectives :  433 ( 145   ~; 124   |; 124   &)
%                                         (  18 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   8 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   4 con; 0-2 aty)
%            Number of variables   :  206 ( 163   !;  43   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f977,plain,
    $false,
    inference(subsumption_resolution,[],[f975,f150]) ).

fof(f150,plain,
    member(sK9,sK10),
    inference(cnf_transformation,[],[f87]) ).

fof(f87,plain,
    ( member(sK10,on)
    & member(sK9,on)
    & member(sK10,sK9)
    & member(sK9,sK10) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f85,f86]) ).

fof(f86,plain,
    ( ? [X0,X1] :
        ( member(X1,on)
        & member(X0,on)
        & member(X1,X0)
        & member(X0,X1) )
   => ( member(sK10,on)
      & member(sK9,on)
      & member(sK10,sK9)
      & member(sK9,sK10) ) ),
    introduced(choice_axiom,[]) ).

fof(f85,plain,
    ? [X0,X1] :
      ( member(X1,on)
      & member(X0,on)
      & member(X1,X0)
      & member(X0,X1) ),
    inference(rectify,[],[f48]) ).

fof(f48,plain,
    ? [X1,X0] :
      ( member(X0,on)
      & member(X1,on)
      & member(X0,X1)
      & member(X1,X0) ),
    inference(flattening,[],[f47]) ).

fof(f47,plain,
    ? [X1,X0] :
      ( member(X0,X1)
      & member(X1,X0)
      & member(X0,on)
      & member(X1,on) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f30,plain,
    ~ ! [X1,X0] :
        ( ( member(X0,on)
          & member(X1,on) )
       => ~ ( member(X0,X1)
            & member(X1,X0) ) ),
    inference(rectify,[],[f21]) ).

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

fof(f20,conjecture,
    ! [X1,X0] :
      ( ( member(X0,on)
        & member(X1,on) )
     => ~ ( member(X1,X0)
          & member(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thV3) ).

fof(f975,plain,
    ~ member(sK9,sK10),
    inference(resolution,[],[f564,f191]) ).

fof(f191,plain,
    strict_order(member_predicate,sK10),
    inference(resolution,[],[f173,f189]) ).

fof(f189,plain,
    strict_well_order(member_predicate,sK10),
    inference(resolution,[],[f126,f153]) ).

fof(f153,plain,
    member(sK10,on),
    inference(cnf_transformation,[],[f87]) ).

fof(f126,plain,
    ! [X0] :
      ( ~ member(X0,on)
      | strict_well_order(member_predicate,X0) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f67,plain,
    ! [X0] :
      ( ( ( set(X0)
          & ! [X1] :
              ( subset(X1,X0)
              | ~ member(X1,X0) )
          & strict_well_order(member_predicate,X0) )
        | ~ member(X0,on) )
      & ( member(X0,on)
        | ~ set(X0)
        | ( ~ subset(sK2(X0),X0)
          & member(sK2(X0),X0) )
        | ~ strict_well_order(member_predicate,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f65,f66]) ).

fof(f66,plain,
    ! [X0] :
      ( ? [X2] :
          ( ~ subset(X2,X0)
          & member(X2,X0) )
     => ( ~ subset(sK2(X0),X0)
        & member(sK2(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f65,plain,
    ! [X0] :
      ( ( ( set(X0)
          & ! [X1] :
              ( subset(X1,X0)
              | ~ member(X1,X0) )
          & strict_well_order(member_predicate,X0) )
        | ~ member(X0,on) )
      & ( member(X0,on)
        | ~ set(X0)
        | ? [X2] :
            ( ~ subset(X2,X0)
            & member(X2,X0) )
        | ~ strict_well_order(member_predicate,X0) ) ),
    inference(rectify,[],[f64]) ).

fof(f64,plain,
    ! [X0] :
      ( ( ( set(X0)
          & ! [X1] :
              ( subset(X1,X0)
              | ~ member(X1,X0) )
          & strict_well_order(member_predicate,X0) )
        | ~ member(X0,on) )
      & ( member(X0,on)
        | ~ set(X0)
        | ? [X1] :
            ( ~ subset(X1,X0)
            & member(X1,X0) )
        | ~ strict_well_order(member_predicate,X0) ) ),
    inference(flattening,[],[f63]) ).

fof(f63,plain,
    ! [X0] :
      ( ( ( set(X0)
          & ! [X1] :
              ( subset(X1,X0)
              | ~ member(X1,X0) )
          & strict_well_order(member_predicate,X0) )
        | ~ member(X0,on) )
      & ( member(X0,on)
        | ~ set(X0)
        | ? [X1] :
            ( ~ subset(X1,X0)
            & member(X1,X0) )
        | ~ strict_well_order(member_predicate,X0) ) ),
    inference(nnf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0] :
      ( ( set(X0)
        & ! [X1] :
            ( subset(X1,X0)
            | ~ member(X1,X0) )
        & strict_well_order(member_predicate,X0) )
    <=> member(X0,on) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0] :
      ( ( strict_well_order(member_predicate,X0)
        & set(X0)
        & ! [X1] :
            ( member(X1,X0)
           => subset(X1,X0) ) )
    <=> member(X0,on) ),
    inference(rectify,[],[f12]) ).

fof(f12,axiom,
    ! [X0] :
      ( member(X0,on)
    <=> ( strict_well_order(member_predicate,X0)
        & set(X0)
        & ! [X2] :
            ( member(X2,X0)
           => subset(X2,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordinal_number) ).

fof(f173,plain,
    ! [X0,X1] :
      ( ~ strict_well_order(X1,X0)
      | strict_order(X1,X0) ),
    inference(cnf_transformation,[],[f111]) ).

fof(f111,plain,
    ! [X0,X1] :
      ( ( strict_well_order(X1,X0)
        | ~ strict_order(X1,X0)
        | ( subset(sK13(X0,X1),X0)
          & member(sK14(X0,X1),sK13(X0,X1))
          & ! [X4] : ~ least(X4,X1,sK13(X0,X1)) ) )
      & ( ( strict_order(X1,X0)
          & ! [X5] :
              ( ~ subset(X5,X0)
              | ! [X6] : ~ member(X6,X5)
              | least(sK15(X1,X5),X1,X5) ) )
        | ~ strict_well_order(X1,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15])],[f107,f110,f109,f108]) ).

fof(f108,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( subset(X2,X0)
          & ? [X3] : member(X3,X2)
          & ! [X4] : ~ least(X4,X1,X2) )
     => ( subset(sK13(X0,X1),X0)
        & ? [X3] : member(X3,sK13(X0,X1))
        & ! [X4] : ~ least(X4,X1,sK13(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f109,plain,
    ! [X0,X1] :
      ( ? [X3] : member(X3,sK13(X0,X1))
     => member(sK14(X0,X1),sK13(X0,X1)) ),
    introduced(choice_axiom,[]) ).

fof(f110,plain,
    ! [X1,X5] :
      ( ? [X7] : least(X7,X1,X5)
     => least(sK15(X1,X5),X1,X5) ),
    introduced(choice_axiom,[]) ).

fof(f107,plain,
    ! [X0,X1] :
      ( ( strict_well_order(X1,X0)
        | ~ strict_order(X1,X0)
        | ? [X2] :
            ( subset(X2,X0)
            & ? [X3] : member(X3,X2)
            & ! [X4] : ~ least(X4,X1,X2) ) )
      & ( ( strict_order(X1,X0)
          & ! [X5] :
              ( ~ subset(X5,X0)
              | ! [X6] : ~ member(X6,X5)
              | ? [X7] : least(X7,X1,X5) ) )
        | ~ strict_well_order(X1,X0) ) ),
    inference(rectify,[],[f106]) ).

fof(f106,plain,
    ! [X0,X1] :
      ( ( strict_well_order(X1,X0)
        | ~ strict_order(X1,X0)
        | ? [X2] :
            ( subset(X2,X0)
            & ? [X3] : member(X3,X2)
            & ! [X4] : ~ least(X4,X1,X2) ) )
      & ( ( strict_order(X1,X0)
          & ! [X2] :
              ( ~ subset(X2,X0)
              | ! [X3] : ~ member(X3,X2)
              | ? [X4] : least(X4,X1,X2) ) )
        | ~ strict_well_order(X1,X0) ) ),
    inference(flattening,[],[f105]) ).

fof(f105,plain,
    ! [X0,X1] :
      ( ( strict_well_order(X1,X0)
        | ~ strict_order(X1,X0)
        | ? [X2] :
            ( subset(X2,X0)
            & ? [X3] : member(X3,X2)
            & ! [X4] : ~ least(X4,X1,X2) ) )
      & ( ( strict_order(X1,X0)
          & ! [X2] :
              ( ~ subset(X2,X0)
              | ! [X3] : ~ member(X3,X2)
              | ? [X4] : least(X4,X1,X2) ) )
        | ~ strict_well_order(X1,X0) ) ),
    inference(nnf_transformation,[],[f51]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( strict_well_order(X1,X0)
    <=> ( strict_order(X1,X0)
        & ! [X2] :
            ( ~ subset(X2,X0)
            | ! [X3] : ~ member(X3,X2)
            | ? [X4] : least(X4,X1,X2) ) ) ),
    inference(flattening,[],[f50]) ).

fof(f50,plain,
    ! [X1,X0] :
      ( ( strict_order(X1,X0)
        & ! [X2] :
            ( ? [X4] : least(X4,X1,X2)
            | ~ subset(X2,X0)
            | ! [X3] : ~ member(X3,X2) ) )
    <=> strict_well_order(X1,X0) ),
    inference(ennf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X1,X0] :
      ( ( strict_order(X1,X0)
        & ! [X2] :
            ( ( subset(X2,X0)
              & ? [X3] : member(X3,X2) )
           => ? [X4] : least(X4,X1,X2) ) )
    <=> strict_well_order(X1,X0) ),
    inference(rectify,[],[f13]) ).

fof(f13,axiom,
    ! [X3,X5] :
      ( ( strict_order(X5,X3)
        & ! [X0] :
            ( ( ? [X2] : member(X2,X0)
              & subset(X0,X3) )
           => ? [X4] : least(X4,X5,X0) ) )
    <=> strict_well_order(X5,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',strict_well_order) ).

fof(f564,plain,
    ! [X18] :
      ( ~ strict_order(member_predicate,X18)
      | ~ member(sK9,X18) ),
    inference(subsumption_resolution,[],[f545,f243]) ).

fof(f243,plain,
    apply(member_predicate,sK9,sK9),
    inference(resolution,[],[f239,f142]) ).

fof(f142,plain,
    ! [X0,X1] :
      ( ~ member(X0,X1)
      | apply(member_predicate,X0,X1) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( ( member(X0,X1)
        | ~ apply(member_predicate,X0,X1) )
      & ( apply(member_predicate,X0,X1)
        | ~ member(X0,X1) ) ),
    inference(nnf_transformation,[],[f35]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( member(X0,X1)
    <=> apply(member_predicate,X0,X1) ),
    inference(rectify,[],[f15]) ).

fof(f15,axiom,
    ! [X2,X4] :
      ( apply(member_predicate,X2,X4)
    <=> member(X2,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rel_member) ).

fof(f239,plain,
    member(sK9,sK9),
    inference(resolution,[],[f232,f194]) ).

fof(f194,plain,
    subset(sK10,sK9),
    inference(resolution,[],[f192,f151]) ).

fof(f151,plain,
    member(sK10,sK9),
    inference(cnf_transformation,[],[f87]) ).

fof(f192,plain,
    ! [X0] :
      ( ~ member(X0,sK9)
      | subset(X0,sK9) ),
    inference(resolution,[],[f127,f152]) ).

fof(f152,plain,
    member(sK9,on),
    inference(cnf_transformation,[],[f87]) ).

fof(f127,plain,
    ! [X0,X1] :
      ( ~ member(X0,on)
      | ~ member(X1,X0)
      | subset(X1,X0) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f232,plain,
    ! [X8] :
      ( ~ subset(sK10,X8)
      | member(sK9,X8) ),
    inference(resolution,[],[f169,f150]) ).

fof(f169,plain,
    ! [X3,X0,X1] :
      ( ~ member(X3,X1)
      | ~ subset(X1,X0)
      | member(X3,X0) ),
    inference(cnf_transformation,[],[f104]) ).

fof(f104,plain,
    ! [X0,X1] :
      ( ( subset(X1,X0)
        | ( member(sK12(X0,X1),X1)
          & ~ member(sK12(X0,X1),X0) ) )
      & ( ! [X3] :
            ( ~ member(X3,X1)
            | member(X3,X0) )
        | ~ subset(X1,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f102,f103]) ).

fof(f103,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( member(X2,X1)
          & ~ member(X2,X0) )
     => ( member(sK12(X0,X1),X1)
        & ~ member(sK12(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f102,plain,
    ! [X0,X1] :
      ( ( subset(X1,X0)
        | ? [X2] :
            ( member(X2,X1)
            & ~ member(X2,X0) ) )
      & ( ! [X3] :
            ( ~ member(X3,X1)
            | member(X3,X0) )
        | ~ subset(X1,X0) ) ),
    inference(rectify,[],[f101]) ).

fof(f101,plain,
    ! [X0,X1] :
      ( ( subset(X1,X0)
        | ? [X2] :
            ( member(X2,X1)
            & ~ member(X2,X0) ) )
      & ( ! [X2] :
            ( ~ member(X2,X1)
            | member(X2,X0) )
        | ~ subset(X1,X0) ) ),
    inference(nnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( subset(X1,X0)
    <=> ! [X2] :
          ( ~ member(X2,X1)
          | member(X2,X0) ) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( subset(X1,X0)
    <=> ! [X2] :
          ( member(X2,X1)
         => member(X2,X0) ) ),
    inference(rectify,[],[f1]) ).

fof(f1,axiom,
    ! [X1,X0] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).

fof(f545,plain,
    ! [X18] :
      ( ~ strict_order(member_predicate,X18)
      | ~ apply(member_predicate,sK9,sK9)
      | ~ member(sK9,X18) ),
    inference(duplicate_literal_removal,[],[f536]) ).

fof(f536,plain,
    ! [X18] :
      ( ~ member(sK9,X18)
      | ~ apply(member_predicate,sK9,sK9)
      | ~ strict_order(member_predicate,X18)
      | ~ member(sK9,X18) ),
    inference(resolution,[],[f136,f243]) ).

fof(f136,plain,
    ! [X0,X1,X4,X5] :
      ( ~ apply(X1,X5,X4)
      | ~ member(X5,X0)
      | ~ apply(X1,X4,X5)
      | ~ member(X4,X0)
      | ~ strict_order(X1,X0) ),
    inference(cnf_transformation,[],[f76]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( ( strict_order(X1,X0)
        | ~ sP0(X1,X0)
        | ( apply(X1,sK7(X0,X1),sK6(X0,X1))
          & member(sK7(X0,X1),X0)
          & apply(X1,sK6(X0,X1),sK7(X0,X1))
          & member(sK6(X0,X1),X0) ) )
      & ( ( sP0(X1,X0)
          & ! [X4,X5] :
              ( ~ apply(X1,X5,X4)
              | ~ member(X5,X0)
              | ~ apply(X1,X4,X5)
              | ~ member(X4,X0) ) )
        | ~ strict_order(X1,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f74,f75]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( ? [X2,X3] :
          ( apply(X1,X3,X2)
          & member(X3,X0)
          & apply(X1,X2,X3)
          & member(X2,X0) )
     => ( apply(X1,sK7(X0,X1),sK6(X0,X1))
        & member(sK7(X0,X1),X0)
        & apply(X1,sK6(X0,X1),sK7(X0,X1))
        & member(sK6(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( ( strict_order(X1,X0)
        | ~ sP0(X1,X0)
        | ? [X2,X3] :
            ( apply(X1,X3,X2)
            & member(X3,X0)
            & apply(X1,X2,X3)
            & member(X2,X0) ) )
      & ( ( sP0(X1,X0)
          & ! [X4,X5] :
              ( ~ apply(X1,X5,X4)
              | ~ member(X5,X0)
              | ~ apply(X1,X4,X5)
              | ~ member(X4,X0) ) )
        | ~ strict_order(X1,X0) ) ),
    inference(rectify,[],[f73]) ).

fof(f73,plain,
    ! [X0,X1] :
      ( ( strict_order(X1,X0)
        | ~ sP0(X1,X0)
        | ? [X5,X6] :
            ( apply(X1,X6,X5)
            & member(X6,X0)
            & apply(X1,X5,X6)
            & member(X5,X0) ) )
      & ( ( sP0(X1,X0)
          & ! [X5,X6] :
              ( ~ apply(X1,X6,X5)
              | ~ member(X6,X0)
              | ~ apply(X1,X5,X6)
              | ~ member(X5,X0) ) )
        | ~ strict_order(X1,X0) ) ),
    inference(flattening,[],[f72]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( ( strict_order(X1,X0)
        | ~ sP0(X1,X0)
        | ? [X5,X6] :
            ( apply(X1,X6,X5)
            & member(X6,X0)
            & apply(X1,X5,X6)
            & member(X5,X0) ) )
      & ( ( sP0(X1,X0)
          & ! [X5,X6] :
              ( ~ apply(X1,X6,X5)
              | ~ member(X6,X0)
              | ~ apply(X1,X5,X6)
              | ~ member(X5,X0) ) )
        | ~ strict_order(X1,X0) ) ),
    inference(nnf_transformation,[],[f55]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( strict_order(X1,X0)
    <=> ( sP0(X1,X0)
        & ! [X5,X6] :
            ( ~ apply(X1,X6,X5)
            | ~ member(X6,X0)
            | ~ apply(X1,X5,X6)
            | ~ member(X5,X0) ) ) ),
    inference(definition_folding,[],[f43,f54]) ).

fof(f54,plain,
    ! [X1,X0] :
      ( sP0(X1,X0)
    <=> ! [X4,X2,X3] :
          ( apply(X1,X4,X2)
          | ~ member(X2,X0)
          | ~ member(X3,X0)
          | ~ apply(X1,X3,X2)
          | ~ apply(X1,X4,X3)
          | ~ member(X4,X0) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( strict_order(X1,X0)
    <=> ( ! [X4,X2,X3] :
            ( apply(X1,X4,X2)
            | ~ member(X2,X0)
            | ~ member(X3,X0)
            | ~ apply(X1,X3,X2)
            | ~ apply(X1,X4,X3)
            | ~ member(X4,X0) )
        & ! [X5,X6] :
            ( ~ apply(X1,X6,X5)
            | ~ member(X6,X0)
            | ~ apply(X1,X5,X6)
            | ~ member(X5,X0) ) ) ),
    inference(flattening,[],[f42]) ).

fof(f42,plain,
    ! [X1,X0] :
      ( strict_order(X1,X0)
    <=> ( ! [X2,X3,X4] :
            ( apply(X1,X4,X2)
            | ~ apply(X1,X3,X2)
            | ~ apply(X1,X4,X3)
            | ~ member(X3,X0)
            | ~ member(X4,X0)
            | ~ member(X2,X0) )
        & ! [X5,X6] :
            ( ~ apply(X1,X5,X6)
            | ~ apply(X1,X6,X5)
            | ~ member(X5,X0)
            | ~ member(X6,X0) ) ) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X1,X0] :
      ( strict_order(X1,X0)
    <=> ( ! [X2,X3,X4] :
            ( ( member(X3,X0)
              & member(X4,X0)
              & member(X2,X0) )
           => ( ( apply(X1,X3,X2)
                & apply(X1,X4,X3) )
             => apply(X1,X4,X2) ) )
        & ! [X5,X6] :
            ( ( member(X5,X0)
              & member(X6,X0) )
           => ~ ( apply(X1,X5,X6)
                & apply(X1,X6,X5) ) ) ) ),
    inference(rectify,[],[f16]) ).

fof(f16,axiom,
    ! [X3,X5] :
      ( ( ! [X7,X4,X2] :
            ( ( member(X2,X3)
              & member(X7,X3)
              & member(X4,X3) )
           => ( ( apply(X5,X2,X4)
                & apply(X5,X4,X7) )
             => apply(X5,X2,X7) ) )
        & ! [X4,X2] :
            ( ( member(X2,X3)
              & member(X4,X3) )
           => ~ ( apply(X5,X4,X2)
                & apply(X5,X2,X4) ) ) )
    <=> strict_order(X5,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',strict_order) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SET810+4 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n021.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 30 14:21:11 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.49  % (12601)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.19/0.49  % (12602)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.50  % (12604)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.19/0.50  % (12609)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.50  % (12599)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.19/0.50  % (12625)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 1.28/0.51  % (12614)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 1.28/0.51  % (12621)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 1.28/0.51  % (12613)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 1.28/0.52  % (12607)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.28/0.52  % (12615)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.28/0.52  % (12611)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 1.28/0.52  TRYING [1]
% 1.28/0.52  TRYING [2]
% 1.28/0.52  % (12608)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.28/0.52  TRYING [3]
% 1.28/0.52  % (12603)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.42/0.53  % (12626)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 1.42/0.53  % (12619)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 1.42/0.53  % (12605)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.42/0.53  % (12623)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 1.42/0.53  TRYING [1]
% 1.42/0.53  % (12627)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 1.42/0.53  TRYING [2]
% 1.42/0.53  % (12616)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 1.42/0.53  TRYING [3]
% 1.42/0.53  % (12600)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.42/0.54  % (12628)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 1.42/0.54  % (12618)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.42/0.54  % (12607)Instruction limit reached!
% 1.42/0.54  % (12607)------------------------------
% 1.42/0.54  % (12607)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.42/0.54  % (12607)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.42/0.54  % (12607)Termination reason: Unknown
% 1.42/0.54  % (12607)Termination phase: Blocked clause elimination
% 1.42/0.54  
% 1.42/0.54  % (12607)Memory used [KB]: 1023
% 1.42/0.54  % (12607)Time elapsed: 0.004 s
% 1.42/0.54  % (12607)Instructions burned: 3 (million)
% 1.42/0.54  % (12607)------------------------------
% 1.42/0.54  % (12607)------------------------------
% 1.42/0.54  % (12620)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 1.42/0.54  % (12600)Refutation not found, incomplete strategy% (12600)------------------------------
% 1.42/0.54  % (12600)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.42/0.54  % (12600)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.42/0.54  % (12600)Termination reason: Refutation not found, incomplete strategy
% 1.42/0.54  
% 1.42/0.54  % (12600)Memory used [KB]: 5628
% 1.42/0.54  % (12600)Time elapsed: 0.134 s
% 1.42/0.54  % (12600)Instructions burned: 5 (million)
% 1.42/0.54  % (12600)------------------------------
% 1.42/0.54  % (12600)------------------------------
% 1.42/0.54  % (12617)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.42/0.54  % (12622)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 1.42/0.54  % (12610)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.42/0.54  % (12601)Instruction limit reached!
% 1.42/0.54  % (12601)------------------------------
% 1.42/0.54  % (12601)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.42/0.54  % (12601)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.42/0.54  % (12601)Termination reason: Unknown
% 1.42/0.54  % (12601)Termination phase: Saturation
% 1.42/0.54  
% 1.42/0.54  % (12601)Memory used [KB]: 1663
% 1.42/0.54  % (12601)Time elapsed: 0.135 s
% 1.42/0.54  % (12601)Instructions burned: 37 (million)
% 1.42/0.54  % (12601)------------------------------
% 1.42/0.54  % (12601)------------------------------
% 1.42/0.55  TRYING [1]
% 1.42/0.55  TRYING [4]
% 1.42/0.55  % (12606)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 1.42/0.55  % (12612)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.42/0.56  % (12624)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 1.42/0.56  TRYING [2]
% 1.42/0.56  TRYING [4]
% 1.42/0.56  TRYING [3]
% 1.42/0.56  % (12606)Instruction limit reached!
% 1.42/0.56  % (12606)------------------------------
% 1.42/0.56  % (12606)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.42/0.57  TRYING [4]
% 1.42/0.57  % (12606)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.42/0.57  % (12606)Termination reason: Unknown
% 1.42/0.57  % (12606)Termination phase: Saturation
% 1.42/0.57  
% 1.42/0.57  % (12606)Memory used [KB]: 5500
% 1.42/0.57  % (12606)Time elapsed: 0.172 s
% 1.42/0.57  % (12606)Instructions burned: 7 (million)
% 1.42/0.57  % (12606)------------------------------
% 1.42/0.57  % (12606)------------------------------
% 1.42/0.58  % (12603)First to succeed.
% 1.42/0.59  % (12627)Also succeeded, but the first one will report.
% 1.42/0.59  % (12605)Instruction limit reached!
% 1.42/0.59  % (12605)------------------------------
% 1.42/0.59  % (12605)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.42/0.59  % (12603)Refutation found. Thanks to Tanya!
% 1.42/0.59  % SZS status Theorem for theBenchmark
% 1.42/0.59  % SZS output start Proof for theBenchmark
% See solution above
% 1.42/0.59  % (12603)------------------------------
% 1.42/0.59  % (12603)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.42/0.59  % (12603)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.42/0.59  % (12603)Termination reason: Refutation
% 1.42/0.59  
% 1.42/0.59  % (12603)Memory used [KB]: 5884
% 1.42/0.59  % (12603)Time elapsed: 0.167 s
% 1.42/0.59  % (12603)Instructions burned: 33 (million)
% 1.42/0.59  % (12603)------------------------------
% 1.42/0.59  % (12603)------------------------------
% 1.42/0.59  % (12597)Success in time 0.243 s
%------------------------------------------------------------------------------