TSTP Solution File: SEU350+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SEU350+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n001.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 : Thu Aug 31 17:06:20 EDT 2023

% Result   : Theorem 3.13s 1.15s
% Output   : CNFRefutation 3.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   78 (  14 unt;   0 def)
%            Number of atoms       :  318 (  29 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  397 ( 157   ~; 169   |;  51   &)
%                                         (   5 <=>;  13  =>;   0  <=;   2 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   98 (   0 sgn;  48   !;  17   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f7,axiom,
    ! [X0] :
      ( ( latt_str(X0)
        & lattice(X0)
        & ~ empty_carrier(X0) )
     => ! [X1] :
          ( element(X1,the_carrier(X0))
         => cast_to_el_of_LattPOSet(X0,X1) = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattice3) ).

fof(f8,axiom,
    ! [X0] :
      ( ( latt_str(X0)
        & lattice(X0)
        & ~ empty_carrier(X0) )
     => ! [X1] :
          ( element(X1,the_carrier(poset_of_lattice(X0)))
         => cast_to_el_of_lattice(X0,X1) = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_lattice3) ).

fof(f16,axiom,
    ! [X0,X1] :
      ( ( element(X1,the_carrier(poset_of_lattice(X0)))
        & latt_str(X0)
        & lattice(X0)
        & ~ empty_carrier(X0) )
     => element(cast_to_el_of_lattice(X0,X1),the_carrier(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_lattice3) ).

fof(f58,axiom,
    ! [X0,X1] :
      ( ( latt_str(X1)
        & lattice(X1)
        & ~ empty_carrier(X1) )
     => ! [X2] :
          ( element(X2,the_carrier(X1))
         => ( latt_element_smaller(X1,X2,X0)
          <=> relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_lattice3) ).

fof(f59,conjecture,
    ! [X0,X1] :
      ( ( latt_str(X1)
        & lattice(X1)
        & ~ empty_carrier(X1) )
     => ! [X2] :
          ( element(X2,the_carrier(poset_of_lattice(X1)))
         => ( relstr_set_smaller(poset_of_lattice(X1),X0,X2)
          <=> latt_element_smaller(X1,cast_to_el_of_lattice(X1,X2),X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_lattice3) ).

fof(f60,negated_conjecture,
    ~ ! [X0,X1] :
        ( ( latt_str(X1)
          & lattice(X1)
          & ~ empty_carrier(X1) )
       => ! [X2] :
            ( element(X2,the_carrier(poset_of_lattice(X1)))
           => ( relstr_set_smaller(poset_of_lattice(X1),X0,X2)
            <=> latt_element_smaller(X1,cast_to_el_of_lattice(X1,X2),X0) ) ) ),
    inference(negated_conjecture,[],[f59]) ).

fof(f81,plain,
    ! [X0] :
      ( ! [X1] :
          ( cast_to_el_of_LattPOSet(X0,X1) = X1
          | ~ element(X1,the_carrier(X0)) )
      | ~ latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f82,plain,
    ! [X0] :
      ( ! [X1] :
          ( cast_to_el_of_LattPOSet(X0,X1) = X1
          | ~ element(X1,the_carrier(X0)) )
      | ~ latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(flattening,[],[f81]) ).

fof(f83,plain,
    ! [X0] :
      ( ! [X1] :
          ( cast_to_el_of_lattice(X0,X1) = X1
          | ~ element(X1,the_carrier(poset_of_lattice(X0))) )
      | ~ latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f84,plain,
    ! [X0] :
      ( ! [X1] :
          ( cast_to_el_of_lattice(X0,X1) = X1
          | ~ element(X1,the_carrier(poset_of_lattice(X0))) )
      | ~ latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(flattening,[],[f83]) ).

fof(f92,plain,
    ! [X0,X1] :
      ( element(cast_to_el_of_lattice(X0,X1),the_carrier(X0))
      | ~ element(X1,the_carrier(poset_of_lattice(X0)))
      | ~ latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f93,plain,
    ! [X0,X1] :
      ( element(cast_to_el_of_lattice(X0,X1),the_carrier(X0))
      | ~ element(X1,the_carrier(poset_of_lattice(X0)))
      | ~ latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(flattening,[],[f92]) ).

fof(f121,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( latt_element_smaller(X1,X2,X0)
          <=> relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2)) )
          | ~ element(X2,the_carrier(X1)) )
      | ~ latt_str(X1)
      | ~ lattice(X1)
      | empty_carrier(X1) ),
    inference(ennf_transformation,[],[f58]) ).

fof(f122,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( latt_element_smaller(X1,X2,X0)
          <=> relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2)) )
          | ~ element(X2,the_carrier(X1)) )
      | ~ latt_str(X1)
      | ~ lattice(X1)
      | empty_carrier(X1) ),
    inference(flattening,[],[f121]) ).

fof(f123,plain,
    ? [X0,X1] :
      ( ? [X2] :
          ( ( relstr_set_smaller(poset_of_lattice(X1),X0,X2)
          <~> latt_element_smaller(X1,cast_to_el_of_lattice(X1,X2),X0) )
          & element(X2,the_carrier(poset_of_lattice(X1))) )
      & latt_str(X1)
      & lattice(X1)
      & ~ empty_carrier(X1) ),
    inference(ennf_transformation,[],[f60]) ).

fof(f124,plain,
    ? [X0,X1] :
      ( ? [X2] :
          ( ( relstr_set_smaller(poset_of_lattice(X1),X0,X2)
          <~> latt_element_smaller(X1,cast_to_el_of_lattice(X1,X2),X0) )
          & element(X2,the_carrier(poset_of_lattice(X1))) )
      & latt_str(X1)
      & lattice(X1)
      & ~ empty_carrier(X1) ),
    inference(flattening,[],[f123]) ).

fof(f165,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( ( latt_element_smaller(X1,X2,X0)
              | ~ relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2)) )
            & ( relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
              | ~ latt_element_smaller(X1,X2,X0) ) )
          | ~ element(X2,the_carrier(X1)) )
      | ~ latt_str(X1)
      | ~ lattice(X1)
      | empty_carrier(X1) ),
    inference(nnf_transformation,[],[f122]) ).

fof(f166,plain,
    ? [X0,X1] :
      ( ? [X2] :
          ( ( ~ latt_element_smaller(X1,cast_to_el_of_lattice(X1,X2),X0)
            | ~ relstr_set_smaller(poset_of_lattice(X1),X0,X2) )
          & ( latt_element_smaller(X1,cast_to_el_of_lattice(X1,X2),X0)
            | relstr_set_smaller(poset_of_lattice(X1),X0,X2) )
          & element(X2,the_carrier(poset_of_lattice(X1))) )
      & latt_str(X1)
      & lattice(X1)
      & ~ empty_carrier(X1) ),
    inference(nnf_transformation,[],[f124]) ).

fof(f167,plain,
    ? [X0,X1] :
      ( ? [X2] :
          ( ( ~ latt_element_smaller(X1,cast_to_el_of_lattice(X1,X2),X0)
            | ~ relstr_set_smaller(poset_of_lattice(X1),X0,X2) )
          & ( latt_element_smaller(X1,cast_to_el_of_lattice(X1,X2),X0)
            | relstr_set_smaller(poset_of_lattice(X1),X0,X2) )
          & element(X2,the_carrier(poset_of_lattice(X1))) )
      & latt_str(X1)
      & lattice(X1)
      & ~ empty_carrier(X1) ),
    inference(flattening,[],[f166]) ).

fof(f168,plain,
    ( ? [X0,X1] :
        ( ? [X2] :
            ( ( ~ latt_element_smaller(X1,cast_to_el_of_lattice(X1,X2),X0)
              | ~ relstr_set_smaller(poset_of_lattice(X1),X0,X2) )
            & ( latt_element_smaller(X1,cast_to_el_of_lattice(X1,X2),X0)
              | relstr_set_smaller(poset_of_lattice(X1),X0,X2) )
            & element(X2,the_carrier(poset_of_lattice(X1))) )
        & latt_str(X1)
        & lattice(X1)
        & ~ empty_carrier(X1) )
   => ( ? [X2] :
          ( ( ~ latt_element_smaller(sK17,cast_to_el_of_lattice(sK17,X2),sK16)
            | ~ relstr_set_smaller(poset_of_lattice(sK17),sK16,X2) )
          & ( latt_element_smaller(sK17,cast_to_el_of_lattice(sK17,X2),sK16)
            | relstr_set_smaller(poset_of_lattice(sK17),sK16,X2) )
          & element(X2,the_carrier(poset_of_lattice(sK17))) )
      & latt_str(sK17)
      & lattice(sK17)
      & ~ empty_carrier(sK17) ) ),
    introduced(choice_axiom,[]) ).

fof(f169,plain,
    ( ? [X2] :
        ( ( ~ latt_element_smaller(sK17,cast_to_el_of_lattice(sK17,X2),sK16)
          | ~ relstr_set_smaller(poset_of_lattice(sK17),sK16,X2) )
        & ( latt_element_smaller(sK17,cast_to_el_of_lattice(sK17,X2),sK16)
          | relstr_set_smaller(poset_of_lattice(sK17),sK16,X2) )
        & element(X2,the_carrier(poset_of_lattice(sK17))) )
   => ( ( ~ latt_element_smaller(sK17,cast_to_el_of_lattice(sK17,sK18),sK16)
        | ~ relstr_set_smaller(poset_of_lattice(sK17),sK16,sK18) )
      & ( latt_element_smaller(sK17,cast_to_el_of_lattice(sK17,sK18),sK16)
        | relstr_set_smaller(poset_of_lattice(sK17),sK16,sK18) )
      & element(sK18,the_carrier(poset_of_lattice(sK17))) ) ),
    introduced(choice_axiom,[]) ).

fof(f170,plain,
    ( ( ~ latt_element_smaller(sK17,cast_to_el_of_lattice(sK17,sK18),sK16)
      | ~ relstr_set_smaller(poset_of_lattice(sK17),sK16,sK18) )
    & ( latt_element_smaller(sK17,cast_to_el_of_lattice(sK17,sK18),sK16)
      | relstr_set_smaller(poset_of_lattice(sK17),sK16,sK18) )
    & element(sK18,the_carrier(poset_of_lattice(sK17)))
    & latt_str(sK17)
    & lattice(sK17)
    & ~ empty_carrier(sK17) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17,sK18])],[f167,f169,f168]) ).

fof(f183,plain,
    ! [X0,X1] :
      ( cast_to_el_of_LattPOSet(X0,X1) = X1
      | ~ element(X1,the_carrier(X0))
      | ~ latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f82]) ).

fof(f184,plain,
    ! [X0,X1] :
      ( cast_to_el_of_lattice(X0,X1) = X1
      | ~ element(X1,the_carrier(poset_of_lattice(X0)))
      | ~ latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f198,plain,
    ! [X0,X1] :
      ( element(cast_to_el_of_lattice(X0,X1),the_carrier(X0))
      | ~ element(X1,the_carrier(poset_of_lattice(X0)))
      | ~ latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f93]) ).

fof(f259,plain,
    ! [X2,X0,X1] :
      ( relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
      | ~ latt_element_smaller(X1,X2,X0)
      | ~ element(X2,the_carrier(X1))
      | ~ latt_str(X1)
      | ~ lattice(X1)
      | empty_carrier(X1) ),
    inference(cnf_transformation,[],[f165]) ).

fof(f260,plain,
    ! [X2,X0,X1] :
      ( latt_element_smaller(X1,X2,X0)
      | ~ relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
      | ~ element(X2,the_carrier(X1))
      | ~ latt_str(X1)
      | ~ lattice(X1)
      | empty_carrier(X1) ),
    inference(cnf_transformation,[],[f165]) ).

fof(f261,plain,
    ~ empty_carrier(sK17),
    inference(cnf_transformation,[],[f170]) ).

fof(f262,plain,
    lattice(sK17),
    inference(cnf_transformation,[],[f170]) ).

fof(f263,plain,
    latt_str(sK17),
    inference(cnf_transformation,[],[f170]) ).

fof(f264,plain,
    element(sK18,the_carrier(poset_of_lattice(sK17))),
    inference(cnf_transformation,[],[f170]) ).

fof(f265,plain,
    ( latt_element_smaller(sK17,cast_to_el_of_lattice(sK17,sK18),sK16)
    | relstr_set_smaller(poset_of_lattice(sK17),sK16,sK18) ),
    inference(cnf_transformation,[],[f170]) ).

fof(f266,plain,
    ( ~ latt_element_smaller(sK17,cast_to_el_of_lattice(sK17,sK18),sK16)
    | ~ relstr_set_smaller(poset_of_lattice(sK17),sK16,sK18) ),
    inference(cnf_transformation,[],[f170]) ).

cnf(c_59,plain,
    ( ~ element(X0,the_carrier(X1))
    | ~ lattice(X1)
    | ~ latt_str(X1)
    | cast_to_el_of_LattPOSet(X1,X0) = X0
    | empty_carrier(X1) ),
    inference(cnf_transformation,[],[f183]) ).

cnf(c_60,plain,
    ( ~ element(X0,the_carrier(poset_of_lattice(X1)))
    | ~ lattice(X1)
    | ~ latt_str(X1)
    | cast_to_el_of_lattice(X1,X0) = X0
    | empty_carrier(X1) ),
    inference(cnf_transformation,[],[f184]) ).

cnf(c_74,plain,
    ( ~ element(X0,the_carrier(poset_of_lattice(X1)))
    | ~ lattice(X1)
    | ~ latt_str(X1)
    | element(cast_to_el_of_lattice(X1,X0),the_carrier(X1))
    | empty_carrier(X1) ),
    inference(cnf_transformation,[],[f198]) ).

cnf(c_135,plain,
    ( ~ relstr_set_smaller(poset_of_lattice(X0),X1,cast_to_el_of_LattPOSet(X0,X2))
    | ~ element(X2,the_carrier(X0))
    | ~ lattice(X0)
    | ~ latt_str(X0)
    | latt_element_smaller(X0,X2,X1)
    | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f260]) ).

cnf(c_136,plain,
    ( ~ latt_element_smaller(X0,X1,X2)
    | ~ element(X1,the_carrier(X0))
    | ~ lattice(X0)
    | ~ latt_str(X0)
    | relstr_set_smaller(poset_of_lattice(X0),X2,cast_to_el_of_LattPOSet(X0,X1))
    | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f259]) ).

cnf(c_137,negated_conjecture,
    ( ~ latt_element_smaller(sK17,cast_to_el_of_lattice(sK17,sK18),sK16)
    | ~ relstr_set_smaller(poset_of_lattice(sK17),sK16,sK18) ),
    inference(cnf_transformation,[],[f266]) ).

cnf(c_138,negated_conjecture,
    ( latt_element_smaller(sK17,cast_to_el_of_lattice(sK17,sK18),sK16)
    | relstr_set_smaller(poset_of_lattice(sK17),sK16,sK18) ),
    inference(cnf_transformation,[],[f265]) ).

cnf(c_139,negated_conjecture,
    element(sK18,the_carrier(poset_of_lattice(sK17))),
    inference(cnf_transformation,[],[f264]) ).

cnf(c_140,negated_conjecture,
    latt_str(sK17),
    inference(cnf_transformation,[],[f263]) ).

cnf(c_141,negated_conjecture,
    lattice(sK17),
    inference(cnf_transformation,[],[f262]) ).

cnf(c_142,negated_conjecture,
    ~ empty_carrier(sK17),
    inference(cnf_transformation,[],[f261]) ).

cnf(c_223,plain,
    ( ~ relstr_set_smaller(poset_of_lattice(sK17),sK16,sK18)
    | ~ latt_element_smaller(sK17,cast_to_el_of_lattice(sK17,sK18),sK16) ),
    inference(prop_impl_just,[status(thm)],[c_137]) ).

cnf(c_224,plain,
    ( ~ latt_element_smaller(sK17,cast_to_el_of_lattice(sK17,sK18),sK16)
    | ~ relstr_set_smaller(poset_of_lattice(sK17),sK16,sK18) ),
    inference(renaming,[status(thm)],[c_223]) ).

cnf(c_225,plain,
    ( relstr_set_smaller(poset_of_lattice(sK17),sK16,sK18)
    | latt_element_smaller(sK17,cast_to_el_of_lattice(sK17,sK18),sK16) ),
    inference(prop_impl_just,[status(thm)],[c_138]) ).

cnf(c_226,plain,
    ( latt_element_smaller(sK17,cast_to_el_of_lattice(sK17,sK18),sK16)
    | relstr_set_smaller(poset_of_lattice(sK17),sK16,sK18) ),
    inference(renaming,[status(thm)],[c_225]) ).

cnf(c_1616,plain,
    ( cast_to_el_of_lattice(sK17,sK18) != X2
    | X0 != sK17
    | X1 != sK16
    | ~ relstr_set_smaller(poset_of_lattice(X0),X1,cast_to_el_of_LattPOSet(X0,X2))
    | ~ relstr_set_smaller(poset_of_lattice(sK17),sK16,sK18)
    | ~ element(X2,the_carrier(X0))
    | ~ lattice(X0)
    | ~ latt_str(X0)
    | empty_carrier(X0) ),
    inference(resolution_lifted,[status(thm)],[c_135,c_224]) ).

cnf(c_1617,plain,
    ( ~ relstr_set_smaller(poset_of_lattice(sK17),sK16,cast_to_el_of_LattPOSet(sK17,cast_to_el_of_lattice(sK17,sK18)))
    | ~ element(cast_to_el_of_lattice(sK17,sK18),the_carrier(sK17))
    | ~ relstr_set_smaller(poset_of_lattice(sK17),sK16,sK18)
    | ~ lattice(sK17)
    | ~ latt_str(sK17)
    | empty_carrier(sK17) ),
    inference(unflattening,[status(thm)],[c_1616]) ).

cnf(c_1618,plain,
    ( ~ relstr_set_smaller(poset_of_lattice(sK17),sK16,sK18)
    | ~ element(cast_to_el_of_lattice(sK17,sK18),the_carrier(sK17))
    | ~ relstr_set_smaller(poset_of_lattice(sK17),sK16,cast_to_el_of_LattPOSet(sK17,cast_to_el_of_lattice(sK17,sK18))) ),
    inference(global_subsumption_just,[status(thm)],[c_1617,c_141,c_140,c_142,c_1617]) ).

cnf(c_1619,plain,
    ( ~ relstr_set_smaller(poset_of_lattice(sK17),sK16,cast_to_el_of_LattPOSet(sK17,cast_to_el_of_lattice(sK17,sK18)))
    | ~ element(cast_to_el_of_lattice(sK17,sK18),the_carrier(sK17))
    | ~ relstr_set_smaller(poset_of_lattice(sK17),sK16,sK18) ),
    inference(renaming,[status(thm)],[c_1618]) ).

cnf(c_1629,plain,
    ( cast_to_el_of_lattice(sK17,sK18) != X1
    | X0 != sK17
    | X2 != sK16
    | ~ element(X1,the_carrier(X0))
    | ~ lattice(X0)
    | ~ latt_str(X0)
    | relstr_set_smaller(poset_of_lattice(X0),X2,cast_to_el_of_LattPOSet(X0,X1))
    | relstr_set_smaller(poset_of_lattice(sK17),sK16,sK18)
    | empty_carrier(X0) ),
    inference(resolution_lifted,[status(thm)],[c_136,c_226]) ).

cnf(c_1630,plain,
    ( ~ element(cast_to_el_of_lattice(sK17,sK18),the_carrier(sK17))
    | ~ lattice(sK17)
    | ~ latt_str(sK17)
    | relstr_set_smaller(poset_of_lattice(sK17),sK16,cast_to_el_of_LattPOSet(sK17,cast_to_el_of_lattice(sK17,sK18)))
    | relstr_set_smaller(poset_of_lattice(sK17),sK16,sK18)
    | empty_carrier(sK17) ),
    inference(unflattening,[status(thm)],[c_1629]) ).

cnf(c_1631,plain,
    ( relstr_set_smaller(poset_of_lattice(sK17),sK16,sK18)
    | relstr_set_smaller(poset_of_lattice(sK17),sK16,cast_to_el_of_LattPOSet(sK17,cast_to_el_of_lattice(sK17,sK18)))
    | ~ element(cast_to_el_of_lattice(sK17,sK18),the_carrier(sK17)) ),
    inference(global_subsumption_just,[status(thm)],[c_1630,c_141,c_140,c_142,c_1630]) ).

cnf(c_1632,plain,
    ( ~ element(cast_to_el_of_lattice(sK17,sK18),the_carrier(sK17))
    | relstr_set_smaller(poset_of_lattice(sK17),sK16,cast_to_el_of_LattPOSet(sK17,cast_to_el_of_lattice(sK17,sK18)))
    | relstr_set_smaller(poset_of_lattice(sK17),sK16,sK18) ),
    inference(renaming,[status(thm)],[c_1631]) ).

cnf(c_1697,plain,
    ( X0 != sK17
    | ~ element(X1,the_carrier(poset_of_lattice(X0)))
    | ~ latt_str(X0)
    | element(cast_to_el_of_lattice(X0,X1),the_carrier(X0))
    | empty_carrier(X0) ),
    inference(resolution_lifted,[status(thm)],[c_74,c_141]) ).

cnf(c_1698,plain,
    ( ~ element(X0,the_carrier(poset_of_lattice(sK17)))
    | ~ latt_str(sK17)
    | element(cast_to_el_of_lattice(sK17,X0),the_carrier(sK17))
    | empty_carrier(sK17) ),
    inference(unflattening,[status(thm)],[c_1697]) ).

cnf(c_1700,plain,
    ( element(cast_to_el_of_lattice(sK17,X0),the_carrier(sK17))
    | ~ element(X0,the_carrier(poset_of_lattice(sK17))) ),
    inference(global_subsumption_just,[status(thm)],[c_1698,c_140,c_142,c_1698]) ).

cnf(c_1701,plain,
    ( ~ element(X0,the_carrier(poset_of_lattice(sK17)))
    | element(cast_to_el_of_lattice(sK17,X0),the_carrier(sK17)) ),
    inference(renaming,[status(thm)],[c_1700]) ).

cnf(c_1721,plain,
    ( X0 != sK17
    | ~ element(X1,the_carrier(poset_of_lattice(X0)))
    | ~ latt_str(X0)
    | cast_to_el_of_lattice(X0,X1) = X1
    | empty_carrier(X0) ),
    inference(resolution_lifted,[status(thm)],[c_60,c_141]) ).

cnf(c_1722,plain,
    ( ~ element(X0,the_carrier(poset_of_lattice(sK17)))
    | ~ latt_str(sK17)
    | cast_to_el_of_lattice(sK17,X0) = X0
    | empty_carrier(sK17) ),
    inference(unflattening,[status(thm)],[c_1721]) ).

cnf(c_1724,plain,
    ( cast_to_el_of_lattice(sK17,X0) = X0
    | ~ element(X0,the_carrier(poset_of_lattice(sK17))) ),
    inference(global_subsumption_just,[status(thm)],[c_1722,c_140,c_142,c_1722]) ).

cnf(c_1725,plain,
    ( ~ element(X0,the_carrier(poset_of_lattice(sK17)))
    | cast_to_el_of_lattice(sK17,X0) = X0 ),
    inference(renaming,[status(thm)],[c_1724]) ).

cnf(c_1733,plain,
    ( X0 != sK17
    | ~ element(X1,the_carrier(X0))
    | ~ latt_str(X0)
    | cast_to_el_of_LattPOSet(X0,X1) = X1
    | empty_carrier(X0) ),
    inference(resolution_lifted,[status(thm)],[c_59,c_141]) ).

cnf(c_1734,plain,
    ( ~ element(X0,the_carrier(sK17))
    | ~ latt_str(sK17)
    | cast_to_el_of_LattPOSet(sK17,X0) = X0
    | empty_carrier(sK17) ),
    inference(unflattening,[status(thm)],[c_1733]) ).

cnf(c_1736,plain,
    ( cast_to_el_of_LattPOSet(sK17,X0) = X0
    | ~ element(X0,the_carrier(sK17)) ),
    inference(global_subsumption_just,[status(thm)],[c_1734,c_140,c_142,c_1734]) ).

cnf(c_1737,plain,
    ( ~ element(X0,the_carrier(sK17))
    | cast_to_el_of_LattPOSet(sK17,X0) = X0 ),
    inference(renaming,[status(thm)],[c_1736]) ).

cnf(c_6066,plain,
    cast_to_el_of_lattice(sK17,sK18) = sK18,
    inference(superposition,[status(thm)],[c_139,c_1725]) ).

cnf(c_6071,plain,
    ( ~ element(sK18,the_carrier(poset_of_lattice(sK17)))
    | element(sK18,the_carrier(sK17)) ),
    inference(superposition,[status(thm)],[c_6066,c_1701]) ).

cnf(c_6072,plain,
    element(sK18,the_carrier(sK17)),
    inference(forward_subsumption_resolution,[status(thm)],[c_6071,c_139]) ).

cnf(c_6073,plain,
    cast_to_el_of_LattPOSet(sK17,sK18) = sK18,
    inference(superposition,[status(thm)],[c_6072,c_1737]) ).

cnf(c_6528,plain,
    ( ~ relstr_set_smaller(poset_of_lattice(sK17),sK16,sK18)
    | ~ element(sK18,the_carrier(sK17)) ),
    inference(light_normalisation,[status(thm)],[c_1619,c_6066,c_6073]) ).

cnf(c_6529,plain,
    ~ relstr_set_smaller(poset_of_lattice(sK17),sK16,sK18),
    inference(forward_subsumption_resolution,[status(thm)],[c_6528,c_6072]) ).

cnf(c_6718,plain,
    ( ~ element(sK18,the_carrier(poset_of_lattice(sK17)))
    | element(cast_to_el_of_lattice(sK17,sK18),the_carrier(sK17)) ),
    inference(instantiation,[status(thm)],[c_1701]) ).

cnf(c_6732,plain,
    ( relstr_set_smaller(poset_of_lattice(sK17),sK16,cast_to_el_of_LattPOSet(sK17,cast_to_el_of_lattice(sK17,sK18)))
    | relstr_set_smaller(poset_of_lattice(sK17),sK16,sK18) ),
    inference(global_subsumption_just,[status(thm)],[c_1632,c_139,c_1632,c_6718]) ).

cnf(c_6734,plain,
    relstr_set_smaller(poset_of_lattice(sK17),sK16,sK18),
    inference(light_normalisation,[status(thm)],[c_6732,c_6066,c_6073]) ).

cnf(c_6735,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_6734,c_6529]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : SEU350+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15  % Command  : run_iprover %s %d THM
% 0.15/0.35  % Computer : n001.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Wed Aug 23 16:56:25 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 0.20/0.47  Running first-order theorem proving
% 0.20/0.47  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.13/1.15  % SZS status Started for theBenchmark.p
% 3.13/1.15  % SZS status Theorem for theBenchmark.p
% 3.13/1.15  
% 3.13/1.15  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.13/1.15  
% 3.13/1.15  ------  iProver source info
% 3.13/1.15  
% 3.13/1.15  git: date: 2023-05-31 18:12:56 +0000
% 3.13/1.15  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.13/1.15  git: non_committed_changes: false
% 3.13/1.15  git: last_make_outside_of_git: false
% 3.13/1.15  
% 3.13/1.15  ------ Parsing...
% 3.13/1.15  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.13/1.15  
% 3.13/1.15  ------ Preprocessing... sup_sim: 0  sf_s  rm: 25 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e  sup_sim: 0  sf_s  rm: 15 0s  sf_e  pe_s  pe_e 
% 3.13/1.15  
% 3.13/1.15  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.13/1.15  
% 3.13/1.15  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.13/1.15  ------ Proving...
% 3.13/1.15  ------ Problem Properties 
% 3.13/1.15  
% 3.13/1.15  
% 3.13/1.15  clauses                                 74
% 3.13/1.15  conjectures                             2
% 3.13/1.15  EPR                                     17
% 3.13/1.15  Horn                                    65
% 3.13/1.15  unary                                   33
% 3.13/1.15  binary                                  27
% 3.13/1.15  lits                                    129
% 3.13/1.15  lits eq                                 11
% 3.13/1.15  fd_pure                                 0
% 3.13/1.15  fd_pseudo                               0
% 3.13/1.15  fd_cond                                 1
% 3.13/1.15  fd_pseudo_cond                          3
% 3.13/1.15  AC symbols                              0
% 3.13/1.15  
% 3.13/1.15  ------ Schedule dynamic 5 is on 
% 3.13/1.15  
% 3.13/1.15  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.13/1.15  
% 3.13/1.15  
% 3.13/1.15  ------ 
% 3.13/1.15  Current options:
% 3.13/1.15  ------ 
% 3.13/1.15  
% 3.13/1.15  
% 3.13/1.15  
% 3.13/1.15  
% 3.13/1.15  ------ Proving...
% 3.13/1.15  
% 3.13/1.15  
% 3.13/1.15  % SZS status Theorem for theBenchmark.p
% 3.13/1.15  
% 3.13/1.15  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.13/1.15  
% 3.13/1.15  
%------------------------------------------------------------------------------