TSTP Solution File: SEU348+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SEU348+1 : TPTP v8.1.0. Released v3.3.0.
% 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 : n017.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 18:33:21 EDT 2022

% Result   : Theorem 1.51s 0.55s
% Output   : Refutation 1.51s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   79 (  16 unt;   3 typ;   0 def)
%            Number of atoms       :  305 (  18 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  371 ( 142   ~; 152   |;  57   &)
%                                         (   5 <=>;  13  =>;   0  <=;   2 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    4 (   0 usr;   3 ari)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :  100 (  80   !;  20   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(pred_def_32,type,
    sQ20_eqProxy: ( $int * $int ) > $o ).

tff(pred_def_33,type,
    sQ21_eqProxy: ( $rat * $rat ) > $o ).

tff(pred_def_34,type,
    sQ22_eqProxy: ( $real * $real ) > $o ).

fof(f671,plain,
    $false,
    inference(subsumption_resolution,[],[f669,f663]) ).

fof(f663,plain,
    ~ relstr_element_smaller(poset_of_lattice(sK9),sK10,sK11),
    inference(subsumption_resolution,[],[f609,f662]) ).

fof(f662,plain,
    latt_set_smaller(sK9,sK11,sK10),
    inference(duplicate_literal_removal,[],[f661]) ).

fof(f661,plain,
    ( latt_set_smaller(sK9,sK11,sK10)
    | latt_set_smaller(sK9,sK11,sK10) ),
    inference(resolution,[],[f660,f608]) ).

fof(f608,plain,
    ( relstr_element_smaller(poset_of_lattice(sK9),sK10,sK11)
    | latt_set_smaller(sK9,sK11,sK10) ),
    inference(backward_demodulation,[],[f373,f604]) ).

fof(f604,plain,
    sK11 = cast_to_el_of_lattice(sK9,sK11),
    inference(resolution,[],[f591,f396]) ).

fof(f396,plain,
    element(sK11,the_carrier(poset_of_lattice(sK9))),
    inference(literal_reordering,[],[f251]) ).

fof(f251,plain,
    element(sK11,the_carrier(poset_of_lattice(sK9))),
    inference(cnf_transformation,[],[f172]) ).

fof(f172,plain,
    ( latt_str(sK9)
    & lattice(sK9)
    & ~ empty_carrier(sK9)
    & element(sK11,the_carrier(poset_of_lattice(sK9)))
    & ( ~ relstr_element_smaller(poset_of_lattice(sK9),sK10,sK11)
      | ~ latt_set_smaller(sK9,cast_to_el_of_lattice(sK9,sK11),sK10) )
    & ( relstr_element_smaller(poset_of_lattice(sK9),sK10,sK11)
      | latt_set_smaller(sK9,cast_to_el_of_lattice(sK9,sK11),sK10) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f169,f171,f170]) ).

fof(f170,plain,
    ( ? [X0,X1] :
        ( latt_str(X0)
        & lattice(X0)
        & ~ empty_carrier(X0)
        & ? [X2] :
            ( element(X2,the_carrier(poset_of_lattice(X0)))
            & ( ~ relstr_element_smaller(poset_of_lattice(X0),X1,X2)
              | ~ latt_set_smaller(X0,cast_to_el_of_lattice(X0,X2),X1) )
            & ( relstr_element_smaller(poset_of_lattice(X0),X1,X2)
              | latt_set_smaller(X0,cast_to_el_of_lattice(X0,X2),X1) ) ) )
   => ( latt_str(sK9)
      & lattice(sK9)
      & ~ empty_carrier(sK9)
      & ? [X2] :
          ( element(X2,the_carrier(poset_of_lattice(sK9)))
          & ( ~ relstr_element_smaller(poset_of_lattice(sK9),sK10,X2)
            | ~ latt_set_smaller(sK9,cast_to_el_of_lattice(sK9,X2),sK10) )
          & ( relstr_element_smaller(poset_of_lattice(sK9),sK10,X2)
            | latt_set_smaller(sK9,cast_to_el_of_lattice(sK9,X2),sK10) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f171,plain,
    ( ? [X2] :
        ( element(X2,the_carrier(poset_of_lattice(sK9)))
        & ( ~ relstr_element_smaller(poset_of_lattice(sK9),sK10,X2)
          | ~ latt_set_smaller(sK9,cast_to_el_of_lattice(sK9,X2),sK10) )
        & ( relstr_element_smaller(poset_of_lattice(sK9),sK10,X2)
          | latt_set_smaller(sK9,cast_to_el_of_lattice(sK9,X2),sK10) ) )
   => ( element(sK11,the_carrier(poset_of_lattice(sK9)))
      & ( ~ relstr_element_smaller(poset_of_lattice(sK9),sK10,sK11)
        | ~ latt_set_smaller(sK9,cast_to_el_of_lattice(sK9,sK11),sK10) )
      & ( relstr_element_smaller(poset_of_lattice(sK9),sK10,sK11)
        | latt_set_smaller(sK9,cast_to_el_of_lattice(sK9,sK11),sK10) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f169,plain,
    ? [X0,X1] :
      ( latt_str(X0)
      & lattice(X0)
      & ~ empty_carrier(X0)
      & ? [X2] :
          ( element(X2,the_carrier(poset_of_lattice(X0)))
          & ( ~ relstr_element_smaller(poset_of_lattice(X0),X1,X2)
            | ~ latt_set_smaller(X0,cast_to_el_of_lattice(X0,X2),X1) )
          & ( relstr_element_smaller(poset_of_lattice(X0),X1,X2)
            | latt_set_smaller(X0,cast_to_el_of_lattice(X0,X2),X1) ) ) ),
    inference(rectify,[],[f168]) ).

fof(f168,plain,
    ? [X1,X0] :
      ( latt_str(X1)
      & lattice(X1)
      & ~ empty_carrier(X1)
      & ? [X2] :
          ( element(X2,the_carrier(poset_of_lattice(X1)))
          & ( ~ relstr_element_smaller(poset_of_lattice(X1),X0,X2)
            | ~ latt_set_smaller(X1,cast_to_el_of_lattice(X1,X2),X0) )
          & ( relstr_element_smaller(poset_of_lattice(X1),X0,X2)
            | latt_set_smaller(X1,cast_to_el_of_lattice(X1,X2),X0) ) ) ),
    inference(flattening,[],[f167]) ).

fof(f167,plain,
    ? [X1,X0] :
      ( latt_str(X1)
      & lattice(X1)
      & ~ empty_carrier(X1)
      & ? [X2] :
          ( element(X2,the_carrier(poset_of_lattice(X1)))
          & ( ~ relstr_element_smaller(poset_of_lattice(X1),X0,X2)
            | ~ latt_set_smaller(X1,cast_to_el_of_lattice(X1,X2),X0) )
          & ( relstr_element_smaller(poset_of_lattice(X1),X0,X2)
            | latt_set_smaller(X1,cast_to_el_of_lattice(X1,X2),X0) ) ) ),
    inference(nnf_transformation,[],[f128]) ).

fof(f128,plain,
    ? [X1,X0] :
      ( latt_str(X1)
      & lattice(X1)
      & ~ empty_carrier(X1)
      & ? [X2] :
          ( element(X2,the_carrier(poset_of_lattice(X1)))
          & ( latt_set_smaller(X1,cast_to_el_of_lattice(X1,X2),X0)
          <~> relstr_element_smaller(poset_of_lattice(X1),X0,X2) ) ) ),
    inference(flattening,[],[f127]) ).

fof(f127,plain,
    ? [X1,X0] :
      ( ? [X2] :
          ( element(X2,the_carrier(poset_of_lattice(X1)))
          & ( latt_set_smaller(X1,cast_to_el_of_lattice(X1,X2),X0)
          <~> relstr_element_smaller(poset_of_lattice(X1),X0,X2) ) )
      & latt_str(X1)
      & ~ empty_carrier(X1)
      & lattice(X1) ),
    inference(ennf_transformation,[],[f59]) ).

fof(f59,negated_conjecture,
    ~ ! [X1,X0] :
        ( ( latt_str(X1)
          & ~ empty_carrier(X1)
          & lattice(X1) )
       => ! [X2] :
            ( element(X2,the_carrier(poset_of_lattice(X1)))
           => ( relstr_element_smaller(poset_of_lattice(X1),X0,X2)
            <=> latt_set_smaller(X1,cast_to_el_of_lattice(X1,X2),X0) ) ) ),
    inference(negated_conjecture,[],[f58]) ).

fof(f58,conjecture,
    ! [X1,X0] :
      ( ( latt_str(X1)
        & ~ empty_carrier(X1)
        & lattice(X1) )
     => ! [X2] :
          ( element(X2,the_carrier(poset_of_lattice(X1)))
         => ( relstr_element_smaller(poset_of_lattice(X1),X0,X2)
          <=> latt_set_smaller(X1,cast_to_el_of_lattice(X1,X2),X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_lattice3) ).

fof(f591,plain,
    ! [X0] :
      ( ~ element(X0,the_carrier(poset_of_lattice(sK9)))
      | cast_to_el_of_lattice(sK9,X0) = X0 ),
    inference(subsumption_resolution,[],[f590,f305]) ).

fof(f305,plain,
    latt_str(sK9),
    inference(literal_reordering,[],[f254]) ).

fof(f254,plain,
    latt_str(sK9),
    inference(cnf_transformation,[],[f172]) ).

fof(f590,plain,
    ! [X0] :
      ( ~ element(X0,the_carrier(poset_of_lattice(sK9)))
      | ~ latt_str(sK9)
      | cast_to_el_of_lattice(sK9,X0) = X0 ),
    inference(subsumption_resolution,[],[f589,f328]) ).

fof(f328,plain,
    ~ empty_carrier(sK9),
    inference(literal_reordering,[],[f252]) ).

fof(f252,plain,
    ~ empty_carrier(sK9),
    inference(cnf_transformation,[],[f172]) ).

fof(f589,plain,
    ! [X0] :
      ( ~ element(X0,the_carrier(poset_of_lattice(sK9)))
      | empty_carrier(sK9)
      | ~ latt_str(sK9)
      | cast_to_el_of_lattice(sK9,X0) = X0 ),
    inference(resolution,[],[f366,f335]) ).

fof(f335,plain,
    lattice(sK9),
    inference(literal_reordering,[],[f253]) ).

fof(f253,plain,
    lattice(sK9),
    inference(cnf_transformation,[],[f172]) ).

fof(f366,plain,
    ! [X0,X1] :
      ( ~ lattice(X0)
      | empty_carrier(X0)
      | ~ element(X1,the_carrier(poset_of_lattice(X0)))
      | cast_to_el_of_lattice(X0,X1) = X1
      | ~ latt_str(X0) ),
    inference(literal_reordering,[],[f283]) ).

fof(f283,plain,
    ! [X0,X1] :
      ( empty_carrier(X0)
      | ~ element(X1,the_carrier(poset_of_lattice(X0)))
      | ~ lattice(X0)
      | cast_to_el_of_lattice(X0,X1) = X1
      | ~ latt_str(X0) ),
    inference(cnf_transformation,[],[f86]) ).

fof(f86,plain,
    ! [X0] :
      ( ~ lattice(X0)
      | ~ latt_str(X0)
      | ! [X1] :
          ( ~ element(X1,the_carrier(poset_of_lattice(X0)))
          | cast_to_el_of_lattice(X0,X1) = X1 )
      | empty_carrier(X0) ),
    inference(flattening,[],[f85]) ).

fof(f85,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ element(X1,the_carrier(poset_of_lattice(X0)))
          | cast_to_el_of_lattice(X0,X1) = X1 )
      | ~ lattice(X0)
      | empty_carrier(X0)
      | ~ latt_str(X0) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0] :
      ( ( lattice(X0)
        & ~ empty_carrier(X0)
        & latt_str(X0) )
     => ! [X1] :
          ( element(X1,the_carrier(poset_of_lattice(X0)))
         => cast_to_el_of_lattice(X0,X1) = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_lattice3) ).

fof(f373,plain,
    ( relstr_element_smaller(poset_of_lattice(sK9),sK10,sK11)
    | latt_set_smaller(sK9,cast_to_el_of_lattice(sK9,sK11),sK10) ),
    inference(literal_reordering,[],[f249]) ).

fof(f249,plain,
    ( latt_set_smaller(sK9,cast_to_el_of_lattice(sK9,sK11),sK10)
    | relstr_element_smaller(poset_of_lattice(sK9),sK10,sK11) ),
    inference(cnf_transformation,[],[f172]) ).

fof(f660,plain,
    ! [X0] :
      ( ~ relstr_element_smaller(poset_of_lattice(sK9),X0,sK11)
      | latt_set_smaller(sK9,sK11,X0) ),
    inference(subsumption_resolution,[],[f658,f653]) ).

fof(f653,plain,
    element(sK11,the_carrier(sK9)),
    inference(subsumption_resolution,[],[f651,f396]) ).

fof(f651,plain,
    ( ~ element(sK11,the_carrier(poset_of_lattice(sK9)))
    | element(sK11,the_carrier(sK9)) ),
    inference(superposition,[],[f613,f604]) ).

fof(f613,plain,
    ! [X0] :
      ( element(cast_to_el_of_lattice(sK9,X0),the_carrier(sK9))
      | ~ element(X0,the_carrier(poset_of_lattice(sK9))) ),
    inference(subsumption_resolution,[],[f612,f305]) ).

fof(f612,plain,
    ! [X0] :
      ( ~ latt_str(sK9)
      | element(cast_to_el_of_lattice(sK9,X0),the_carrier(sK9))
      | ~ element(X0,the_carrier(poset_of_lattice(sK9))) ),
    inference(subsumption_resolution,[],[f611,f328]) ).

fof(f611,plain,
    ! [X0] :
      ( empty_carrier(sK9)
      | ~ element(X0,the_carrier(poset_of_lattice(sK9)))
      | ~ latt_str(sK9)
      | element(cast_to_el_of_lattice(sK9,X0),the_carrier(sK9)) ),
    inference(resolution,[],[f347,f335]) ).

fof(f347,plain,
    ! [X0,X1] :
      ( ~ lattice(X0)
      | ~ latt_str(X0)
      | element(cast_to_el_of_lattice(X0,X1),the_carrier(X0))
      | empty_carrier(X0)
      | ~ element(X1,the_carrier(poset_of_lattice(X0))) ),
    inference(literal_reordering,[],[f269]) ).

fof(f269,plain,
    ! [X0,X1] :
      ( element(cast_to_el_of_lattice(X0,X1),the_carrier(X0))
      | empty_carrier(X0)
      | ~ lattice(X0)
      | ~ element(X1,the_carrier(poset_of_lattice(X0)))
      | ~ latt_str(X0) ),
    inference(cnf_transformation,[],[f133]) ).

fof(f133,plain,
    ! [X0,X1] :
      ( ~ element(X1,the_carrier(poset_of_lattice(X0)))
      | element(cast_to_el_of_lattice(X0,X1),the_carrier(X0))
      | ~ lattice(X0)
      | empty_carrier(X0)
      | ~ latt_str(X0) ),
    inference(flattening,[],[f132]) ).

fof(f132,plain,
    ! [X1,X0] :
      ( element(cast_to_el_of_lattice(X0,X1),the_carrier(X0))
      | empty_carrier(X0)
      | ~ element(X1,the_carrier(poset_of_lattice(X0)))
      | ~ latt_str(X0)
      | ~ lattice(X0) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X1,X0] :
      ( ( ~ empty_carrier(X0)
        & element(X1,the_carrier(poset_of_lattice(X0)))
        & latt_str(X0)
        & lattice(X0) )
     => element(cast_to_el_of_lattice(X0,X1),the_carrier(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_lattice3) ).

fof(f658,plain,
    ! [X0] :
      ( ~ element(sK11,the_carrier(sK9))
      | latt_set_smaller(sK9,sK11,X0)
      | ~ relstr_element_smaller(poset_of_lattice(sK9),X0,sK11) ),
    inference(superposition,[],[f649,f654]) ).

fof(f654,plain,
    sK11 = cast_to_el_of_LattPOSet(sK9,sK11),
    inference(resolution,[],[f653,f587]) ).

fof(f587,plain,
    ! [X0] :
      ( ~ element(X0,the_carrier(sK9))
      | cast_to_el_of_LattPOSet(sK9,X0) = X0 ),
    inference(subsumption_resolution,[],[f586,f328]) ).

fof(f586,plain,
    ! [X0] :
      ( cast_to_el_of_LattPOSet(sK9,X0) = X0
      | ~ element(X0,the_carrier(sK9))
      | empty_carrier(sK9) ),
    inference(subsumption_resolution,[],[f585,f305]) ).

fof(f585,plain,
    ! [X0] :
      ( cast_to_el_of_LattPOSet(sK9,X0) = X0
      | ~ latt_str(sK9)
      | ~ element(X0,the_carrier(sK9))
      | empty_carrier(sK9) ),
    inference(resolution,[],[f377,f335]) ).

fof(f377,plain,
    ! [X0,X1] :
      ( ~ lattice(X0)
      | empty_carrier(X0)
      | ~ element(X1,the_carrier(X0))
      | ~ latt_str(X0)
      | cast_to_el_of_LattPOSet(X0,X1) = X1 ),
    inference(literal_reordering,[],[f279]) ).

fof(f279,plain,
    ! [X0,X1] :
      ( ~ latt_str(X0)
      | ~ element(X1,the_carrier(X0))
      | empty_carrier(X0)
      | ~ lattice(X0)
      | cast_to_el_of_LattPOSet(X0,X1) = X1 ),
    inference(cnf_transformation,[],[f139]) ).

fof(f139,plain,
    ! [X0] :
      ( ~ latt_str(X0)
      | empty_carrier(X0)
      | ~ lattice(X0)
      | ! [X1] :
          ( cast_to_el_of_LattPOSet(X0,X1) = X1
          | ~ element(X1,the_carrier(X0)) ) ),
    inference(flattening,[],[f138]) ).

fof(f138,plain,
    ! [X0] :
      ( ! [X1] :
          ( cast_to_el_of_LattPOSet(X0,X1) = X1
          | ~ element(X1,the_carrier(X0)) )
      | empty_carrier(X0)
      | ~ latt_str(X0)
      | ~ lattice(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0] :
      ( ( ~ empty_carrier(X0)
        & latt_str(X0)
        & lattice(X0) )
     => ! [X1] :
          ( element(X1,the_carrier(X0))
         => cast_to_el_of_LattPOSet(X0,X1) = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_lattice3) ).

fof(f649,plain,
    ! [X0,X1] :
      ( ~ relstr_element_smaller(poset_of_lattice(sK9),X1,cast_to_el_of_LattPOSet(sK9,X0))
      | latt_set_smaller(sK9,X0,X1)
      | ~ element(X0,the_carrier(sK9)) ),
    inference(subsumption_resolution,[],[f648,f328]) ).

fof(f648,plain,
    ! [X0,X1] :
      ( latt_set_smaller(sK9,X0,X1)
      | empty_carrier(sK9)
      | ~ element(X0,the_carrier(sK9))
      | ~ relstr_element_smaller(poset_of_lattice(sK9),X1,cast_to_el_of_LattPOSet(sK9,X0)) ),
    inference(subsumption_resolution,[],[f647,f305]) ).

fof(f647,plain,
    ! [X0,X1] :
      ( ~ relstr_element_smaller(poset_of_lattice(sK9),X1,cast_to_el_of_LattPOSet(sK9,X0))
      | ~ element(X0,the_carrier(sK9))
      | ~ latt_str(sK9)
      | latt_set_smaller(sK9,X0,X1)
      | empty_carrier(sK9) ),
    inference(resolution,[],[f381,f335]) ).

fof(f381,plain,
    ! [X2,X0,X1] :
      ( ~ lattice(X0)
      | empty_carrier(X0)
      | ~ latt_str(X0)
      | latt_set_smaller(X0,X2,X1)
      | ~ relstr_element_smaller(poset_of_lattice(X0),X1,cast_to_el_of_LattPOSet(X0,X2))
      | ~ element(X2,the_carrier(X0)) ),
    inference(literal_reordering,[],[f273]) ).

fof(f273,plain,
    ! [X2,X0,X1] :
      ( ~ element(X2,the_carrier(X0))
      | ~ relstr_element_smaller(poset_of_lattice(X0),X1,cast_to_el_of_LattPOSet(X0,X2))
      | latt_set_smaller(X0,X2,X1)
      | ~ lattice(X0)
      | ~ latt_str(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f184]) ).

fof(f184,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( ( relstr_element_smaller(poset_of_lattice(X0),X1,cast_to_el_of_LattPOSet(X0,X2))
              | ~ latt_set_smaller(X0,X2,X1) )
            & ( latt_set_smaller(X0,X2,X1)
              | ~ relstr_element_smaller(poset_of_lattice(X0),X1,cast_to_el_of_LattPOSet(X0,X2)) ) )
          | ~ element(X2,the_carrier(X0)) )
      | empty_carrier(X0)
      | ~ latt_str(X0)
      | ~ lattice(X0) ),
    inference(rectify,[],[f183]) ).

fof(f183,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( ( ( relstr_element_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
              | ~ latt_set_smaller(X1,X2,X0) )
            & ( latt_set_smaller(X1,X2,X0)
              | ~ relstr_element_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2)) ) )
          | ~ element(X2,the_carrier(X1)) )
      | empty_carrier(X1)
      | ~ latt_str(X1)
      | ~ lattice(X1) ),
    inference(nnf_transformation,[],[f96]) ).

fof(f96,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( ( relstr_element_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
          <=> latt_set_smaller(X1,X2,X0) )
          | ~ element(X2,the_carrier(X1)) )
      | empty_carrier(X1)
      | ~ latt_str(X1)
      | ~ lattice(X1) ),
    inference(flattening,[],[f95]) ).

fof(f95,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( relstr_element_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
          <=> latt_set_smaller(X1,X2,X0) )
          | ~ element(X2,the_carrier(X1)) )
      | ~ latt_str(X1)
      | empty_carrier(X1)
      | ~ lattice(X1) ),
    inference(ennf_transformation,[],[f57]) ).

fof(f57,axiom,
    ! [X0,X1] :
      ( ( latt_str(X1)
        & ~ empty_carrier(X1)
        & lattice(X1) )
     => ! [X2] :
          ( element(X2,the_carrier(X1))
         => ( relstr_element_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
          <=> latt_set_smaller(X1,X2,X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_lattice3) ).

fof(f609,plain,
    ( ~ latt_set_smaller(sK9,sK11,sK10)
    | ~ relstr_element_smaller(poset_of_lattice(sK9),sK10,sK11) ),
    inference(backward_demodulation,[],[f319,f604]) ).

fof(f319,plain,
    ( ~ relstr_element_smaller(poset_of_lattice(sK9),sK10,sK11)
    | ~ latt_set_smaller(sK9,cast_to_el_of_lattice(sK9,sK11),sK10) ),
    inference(literal_reordering,[],[f250]) ).

fof(f250,plain,
    ( ~ relstr_element_smaller(poset_of_lattice(sK9),sK10,sK11)
    | ~ latt_set_smaller(sK9,cast_to_el_of_lattice(sK9,sK11),sK10) ),
    inference(cnf_transformation,[],[f172]) ).

fof(f669,plain,
    relstr_element_smaller(poset_of_lattice(sK9),sK10,sK11),
    inference(forward_demodulation,[],[f668,f654]) ).

fof(f668,plain,
    relstr_element_smaller(poset_of_lattice(sK9),sK10,cast_to_el_of_LattPOSet(sK9,sK11)),
    inference(subsumption_resolution,[],[f667,f335]) ).

fof(f667,plain,
    ( relstr_element_smaller(poset_of_lattice(sK9),sK10,cast_to_el_of_LattPOSet(sK9,sK11))
    | ~ lattice(sK9) ),
    inference(subsumption_resolution,[],[f666,f305]) ).

fof(f666,plain,
    ( ~ latt_str(sK9)
    | ~ lattice(sK9)
    | relstr_element_smaller(poset_of_lattice(sK9),sK10,cast_to_el_of_LattPOSet(sK9,sK11)) ),
    inference(subsumption_resolution,[],[f665,f653]) ).

fof(f665,plain,
    ( relstr_element_smaller(poset_of_lattice(sK9),sK10,cast_to_el_of_LattPOSet(sK9,sK11))
    | ~ element(sK11,the_carrier(sK9))
    | ~ latt_str(sK9)
    | ~ lattice(sK9) ),
    inference(subsumption_resolution,[],[f664,f328]) ).

fof(f664,plain,
    ( empty_carrier(sK9)
    | ~ lattice(sK9)
    | ~ element(sK11,the_carrier(sK9))
    | relstr_element_smaller(poset_of_lattice(sK9),sK10,cast_to_el_of_LattPOSet(sK9,sK11))
    | ~ latt_str(sK9) ),
    inference(resolution,[],[f662,f330]) ).

fof(f330,plain,
    ! [X2,X0,X1] :
      ( ~ latt_set_smaller(X0,X2,X1)
      | ~ latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0)
      | ~ element(X2,the_carrier(X0))
      | relstr_element_smaller(poset_of_lattice(X0),X1,cast_to_el_of_LattPOSet(X0,X2)) ),
    inference(literal_reordering,[],[f274]) ).

fof(f274,plain,
    ! [X2,X0,X1] :
      ( relstr_element_smaller(poset_of_lattice(X0),X1,cast_to_el_of_LattPOSet(X0,X2))
      | ~ latt_str(X0)
      | ~ element(X2,the_carrier(X0))
      | empty_carrier(X0)
      | ~ lattice(X0)
      | ~ latt_set_smaller(X0,X2,X1) ),
    inference(cnf_transformation,[],[f184]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEU348+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.34  % Computer : n017.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % 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 14:40:20 EDT 2022
% 0.14/0.35  % CPUTime    : 
% 0.21/0.51  % (2901)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)
% 0.21/0.51  % (2905)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)
% 0.21/0.51  % (2893)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)
% 0.21/0.52  % (2885)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)
% 0.21/0.52  % (2880)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)
% 0.21/0.52  % (2883)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.30/0.53  % (2895)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)
% 1.30/0.53  % (2887)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.30/0.53  % (2897)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.30/0.53  % (2882)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)
% 1.30/0.53  % (2880)Refutation not found, incomplete strategy% (2880)------------------------------
% 1.30/0.53  % (2880)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.30/0.53  % (2880)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.30/0.53  % (2880)Termination reason: Refutation not found, incomplete strategy
% 1.30/0.53  
% 1.30/0.53  % (2880)Memory used [KB]: 5628
% 1.30/0.53  % (2880)Time elapsed: 0.129 s
% 1.30/0.53  % (2880)Instructions burned: 6 (million)
% 1.30/0.53  % (2880)------------------------------
% 1.30/0.53  % (2880)------------------------------
% 1.30/0.53  % (2879)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)
% 1.30/0.53  % (2884)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)
% 1.30/0.53  % (2907)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 1.30/0.53  % (2881)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)
% 1.30/0.53  % (2889)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.30/0.53  % (2888)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)
% 1.30/0.54  % (2887)Instruction limit reached!
% 1.30/0.54  % (2887)------------------------------
% 1.30/0.54  % (2887)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.30/0.54  % (2887)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.30/0.54  % (2887)Termination reason: Unknown
% 1.30/0.54  % (2887)Termination phase: Property scanning
% 1.30/0.54  
% 1.30/0.54  % (2887)Memory used [KB]: 1023
% 1.30/0.54  % (2887)Time elapsed: 0.004 s
% 1.30/0.54  % (2887)Instructions burned: 3 (million)
% 1.30/0.54  % (2887)------------------------------
% 1.30/0.54  % (2887)------------------------------
% 1.30/0.54  % (2899)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)
% 1.30/0.54  % (2893)First to succeed.
% 1.30/0.54  % (2906)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)
% 1.30/0.54  % (2900)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 1.30/0.54  % (2902)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)
% 1.30/0.54  % (2903)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 1.30/0.54  % (2891)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 1.30/0.54  % (2886)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 1.30/0.54  % (2904)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 1.30/0.54  % (2892)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.30/0.55  % (2894)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)
% 1.30/0.55  % (2886)Instruction limit reached!
% 1.30/0.55  % (2886)------------------------------
% 1.30/0.55  % (2886)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.51/0.55  TRYING [1]
% 1.51/0.55  TRYING [1]
% 1.51/0.55  TRYING [2]
% 1.51/0.55  % (2908)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)
% 1.51/0.55  % (2896)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 1.51/0.55  % (2898)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)
% 1.51/0.55  % (2890)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)
% 1.51/0.55  TRYING [3]
% 1.51/0.55  % (2886)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.51/0.55  % (2886)Termination reason: Unknown
% 1.51/0.55  % (2886)Termination phase: Saturation
% 1.51/0.55  
% 1.51/0.55  % (2886)Memory used [KB]: 5628
% 1.51/0.55  % (2886)Time elapsed: 0.136 s
% 1.51/0.55  % (2886)Instructions burned: 8 (million)
% 1.51/0.55  % (2886)------------------------------
% 1.51/0.55  % (2886)------------------------------
% 1.51/0.55  % (2901)Also succeeded, but the first one will report.
% 1.51/0.55  TRYING [2]
% 1.51/0.55  % (2893)Refutation found. Thanks to Tanya!
% 1.51/0.55  % SZS status Theorem for theBenchmark
% 1.51/0.55  % SZS output start Proof for theBenchmark
% See solution above
% 1.51/0.55  % (2893)------------------------------
% 1.51/0.55  % (2893)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.51/0.55  % (2893)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.51/0.55  % (2893)Termination reason: Refutation
% 1.51/0.55  
% 1.51/0.55  % (2893)Memory used [KB]: 6268
% 1.51/0.55  % (2893)Time elapsed: 0.019 s
% 1.51/0.55  % (2893)Instructions burned: 18 (million)
% 1.51/0.55  % (2893)------------------------------
% 1.51/0.55  % (2893)------------------------------
% 1.51/0.55  % (2878)Success in time 0.197 s
%------------------------------------------------------------------------------