TSTP Solution File: SEU347+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SEU347+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n010.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 : Fri May  3 03:05:53 EDT 2024

% Result   : Theorem 170.15s 23.23s
% Output   : CNFRefutation 170.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   25
% Syntax   : Number of formulae    :  241 (  11 unt;   0 def)
%            Number of atoms       : 1280 ( 127 equ)
%            Maximal formula atoms :   16 (   5 avg)
%            Number of connectives : 1759 ( 720   ~; 831   |; 154   &)
%                                         (  18 <=>;  34  =>;   0  <=;   2 <~>)
%            Maximal formula depth :   16 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   30 (  28 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   3 con; 0-3 aty)
%            Number of variables   :  511 (   5 sgn 205   !;  23   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0] :
      ( rel_str(X0)
     => ( strict_rel_str(X0)
       => rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).

fof(f3,axiom,
    ! [X0] :
      ( latt_str(X0)
     => ( ( lattice(X0)
          & ~ empty_carrier(X0) )
       => ( join_absorbing(X0)
          & meet_absorbing(X0)
          & meet_associative(X0)
          & meet_commutative(X0)
          & join_associative(X0)
          & join_commutative(X0)
          & ~ empty_carrier(X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_lattices) ).

fof(f6,axiom,
    ! [X0] :
      ( ( latt_str(X0)
        & ~ empty_carrier(X0) )
     => ! [X1] :
          ( element(X1,the_carrier(X0))
         => ! [X2] :
              ( latt_set_smaller(X0,X1,X2)
            <=> ! [X3] :
                  ( element(X3,the_carrier(X0))
                 => ( in(X3,X2)
                   => below(X0,X1,X3) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_lattice3) ).

fof(f7,axiom,
    ! [X0] :
      ( ( latt_str(X0)
        & lattice(X0)
        & ~ empty_carrier(X0) )
     => poset_of_lattice(X0) = rel_str_of(the_carrier(X0),k2_lattice3(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_lattice3) ).

fof(f8,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(f10,axiom,
    ! [X0] :
      ( rel_str(X0)
     => ! [X1,X2] :
          ( element(X2,the_carrier(X0))
         => ( relstr_element_smaller(X0,X1,X2)
          <=> ! [X3] :
                ( element(X3,the_carrier(X0))
               => ( in(X3,X1)
                 => related(X0,X2,X3) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_lattice3) ).

fof(f14,axiom,
    ! [X0] :
      ( ( latt_str(X0)
        & lattice(X0)
        & ~ empty_carrier(X0) )
     => ( relation_of2_as_subset(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
        & v1_partfun1(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
        & transitive(k2_lattice3(X0))
        & antisymmetric(k2_lattice3(X0))
        & reflexive(k2_lattice3(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_lattice3) ).

fof(f16,axiom,
    ! [X0] :
      ( ( latt_str(X0)
        & lattice(X0)
        & ~ empty_carrier(X0) )
     => ( rel_str(poset_of_lattice(X0))
        & antisymmetric_relstr(poset_of_lattice(X0))
        & transitive_relstr(poset_of_lattice(X0))
        & reflexive_relstr(poset_of_lattice(X0))
        & strict_rel_str(poset_of_lattice(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_lattice3) ).

fof(f17,axiom,
    ! [X0,X1] :
      ( ( element(X1,the_carrier(X0))
        & latt_str(X0)
        & lattice(X0)
        & ~ empty_carrier(X0) )
     => element(cast_to_el_of_LattPOSet(X0,X1),the_carrier(poset_of_lattice(X0))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_lattice3) ).

fof(f44,axiom,
    ! [X0] :
      ( ( latt_str(X0)
        & lattice(X0)
        & ~ empty_carrier(X0) )
     => ( antisymmetric_relstr(poset_of_lattice(X0))
        & transitive_relstr(poset_of_lattice(X0))
        & reflexive_relstr(poset_of_lattice(X0))
        & strict_rel_str(poset_of_lattice(X0))
        & ~ empty_carrier(poset_of_lattice(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_lattice3) ).

fof(f46,axiom,
    ! [X0,X1] :
      ( relation_of2(X1,X0,X0)
     => ! [X2,X3] :
          ( rel_str_of(X0,X1) = rel_str_of(X2,X3)
         => ( X1 = X3
            & X0 = X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_orders_2) ).

fof(f56,axiom,
    ! [X0,X1,X2] :
      ( relation_of2_as_subset(X2,X0,X1)
    <=> relation_of2(X2,X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).

fof(f57,axiom,
    ! [X0,X1,X2] :
      ( ( element(X2,the_carrier(X0))
        & element(X1,the_carrier(X0))
        & latt_str(X0)
        & join_absorbing(X0)
        & meet_absorbing(X0)
        & meet_commutative(X0)
        & ~ empty_carrier(X0) )
     => ( below_refl(X0,X1,X2)
      <=> below(X0,X1,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r3_lattices) ).

fof(f58,axiom,
    ! [X0,X1,X2] :
      ( ( element(X2,the_carrier(X0))
        & element(X1,the_carrier(X0))
        & rel_str(X0)
        & reflexive_relstr(X0)
        & ~ empty_carrier(X0) )
     => ( related_reflexive(X0,X1,X2)
      <=> related(X0,X1,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r3_orders_2) ).

fof(f63,conjecture,
    ! [X0,X1] :
      ( ( latt_str(X1)
        & lattice(X1)
        & ~ empty_carrier(X1) )
     => ! [X2] :
          ( element(X2,the_carrier(X1))
         => ( latt_set_smaller(X1,X2,X0)
          <=> relstr_element_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_lattice3) ).

fof(f64,negated_conjecture,
    ~ ! [X0,X1] :
        ( ( latt_str(X1)
          & lattice(X1)
          & ~ empty_carrier(X1) )
       => ! [X2] :
            ( element(X2,the_carrier(X1))
           => ( latt_set_smaller(X1,X2,X0)
            <=> relstr_element_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2)) ) ) ),
    inference(negated_conjecture,[],[f63]) ).

fof(f71,axiom,
    ! [X0] :
      ( ( latt_str(X0)
        & lattice(X0)
        & ~ empty_carrier(X0) )
     => ! [X1] :
          ( element(X1,the_carrier(X0))
         => ! [X2] :
              ( element(X2,the_carrier(X0))
             => ( below_refl(X0,X1,X2)
              <=> related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_lattice3) ).

fof(f78,plain,
    ! [X0] :
      ( rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
      | ~ strict_rel_str(X0)
      | ~ rel_str(X0) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f79,plain,
    ! [X0] :
      ( rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
      | ~ strict_rel_str(X0)
      | ~ rel_str(X0) ),
    inference(flattening,[],[f78]) ).

fof(f81,plain,
    ! [X0] :
      ( ( join_absorbing(X0)
        & meet_absorbing(X0)
        & meet_associative(X0)
        & meet_commutative(X0)
        & join_associative(X0)
        & join_commutative(X0)
        & ~ empty_carrier(X0) )
      | ~ lattice(X0)
      | empty_carrier(X0)
      | ~ latt_str(X0) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f82,plain,
    ! [X0] :
      ( ( join_absorbing(X0)
        & meet_absorbing(X0)
        & meet_associative(X0)
        & meet_commutative(X0)
        & join_associative(X0)
        & join_commutative(X0)
        & ~ empty_carrier(X0) )
      | ~ lattice(X0)
      | empty_carrier(X0)
      | ~ latt_str(X0) ),
    inference(flattening,[],[f81]) ).

fof(f85,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( latt_set_smaller(X0,X1,X2)
            <=> ! [X3] :
                  ( below(X0,X1,X3)
                  | ~ in(X3,X2)
                  | ~ element(X3,the_carrier(X0)) ) )
          | ~ element(X1,the_carrier(X0)) )
      | ~ latt_str(X0)
      | empty_carrier(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f86,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( latt_set_smaller(X0,X1,X2)
            <=> ! [X3] :
                  ( below(X0,X1,X3)
                  | ~ in(X3,X2)
                  | ~ element(X3,the_carrier(X0)) ) )
          | ~ element(X1,the_carrier(X0)) )
      | ~ latt_str(X0)
      | empty_carrier(X0) ),
    inference(flattening,[],[f85]) ).

fof(f87,plain,
    ! [X0] :
      ( poset_of_lattice(X0) = rel_str_of(the_carrier(X0),k2_lattice3(X0))
      | ~ latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f88,plain,
    ! [X0] :
      ( poset_of_lattice(X0) = rel_str_of(the_carrier(X0),k2_lattice3(X0))
      | ~ latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(flattening,[],[f87]) ).

fof(f89,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,[],[f8]) ).

fof(f90,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,[],[f89]) ).

fof(f93,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( relstr_element_smaller(X0,X1,X2)
          <=> ! [X3] :
                ( related(X0,X2,X3)
                | ~ in(X3,X1)
                | ~ element(X3,the_carrier(X0)) ) )
          | ~ element(X2,the_carrier(X0)) )
      | ~ rel_str(X0) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f94,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( relstr_element_smaller(X0,X1,X2)
          <=> ! [X3] :
                ( related(X0,X2,X3)
                | ~ in(X3,X1)
                | ~ element(X3,the_carrier(X0)) ) )
          | ~ element(X2,the_carrier(X0)) )
      | ~ rel_str(X0) ),
    inference(flattening,[],[f93]) ).

fof(f96,plain,
    ! [X0] :
      ( ( relation_of2_as_subset(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
        & v1_partfun1(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
        & transitive(k2_lattice3(X0))
        & antisymmetric(k2_lattice3(X0))
        & reflexive(k2_lattice3(X0)) )
      | ~ latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f97,plain,
    ! [X0] :
      ( ( relation_of2_as_subset(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
        & v1_partfun1(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
        & transitive(k2_lattice3(X0))
        & antisymmetric(k2_lattice3(X0))
        & reflexive(k2_lattice3(X0)) )
      | ~ latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(flattening,[],[f96]) ).

fof(f98,plain,
    ! [X0] :
      ( ( rel_str(poset_of_lattice(X0))
        & antisymmetric_relstr(poset_of_lattice(X0))
        & transitive_relstr(poset_of_lattice(X0))
        & reflexive_relstr(poset_of_lattice(X0))
        & strict_rel_str(poset_of_lattice(X0)) )
      | ~ latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f99,plain,
    ! [X0] :
      ( ( rel_str(poset_of_lattice(X0))
        & antisymmetric_relstr(poset_of_lattice(X0))
        & transitive_relstr(poset_of_lattice(X0))
        & reflexive_relstr(poset_of_lattice(X0))
        & strict_rel_str(poset_of_lattice(X0)) )
      | ~ latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(flattening,[],[f98]) ).

fof(f100,plain,
    ! [X0,X1] :
      ( element(cast_to_el_of_LattPOSet(X0,X1),the_carrier(poset_of_lattice(X0)))
      | ~ element(X1,the_carrier(X0))
      | ~ latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f101,plain,
    ! [X0,X1] :
      ( element(cast_to_el_of_LattPOSet(X0,X1),the_carrier(poset_of_lattice(X0)))
      | ~ element(X1,the_carrier(X0))
      | ~ latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(flattening,[],[f100]) ).

fof(f118,plain,
    ! [X0] :
      ( ( antisymmetric_relstr(poset_of_lattice(X0))
        & transitive_relstr(poset_of_lattice(X0))
        & reflexive_relstr(poset_of_lattice(X0))
        & strict_rel_str(poset_of_lattice(X0))
        & ~ empty_carrier(poset_of_lattice(X0)) )
      | ~ latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(ennf_transformation,[],[f44]) ).

fof(f119,plain,
    ! [X0] :
      ( ( antisymmetric_relstr(poset_of_lattice(X0))
        & transitive_relstr(poset_of_lattice(X0))
        & reflexive_relstr(poset_of_lattice(X0))
        & strict_rel_str(poset_of_lattice(X0))
        & ~ empty_carrier(poset_of_lattice(X0)) )
      | ~ latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(flattening,[],[f118]) ).

fof(f122,plain,
    ! [X0,X1] :
      ( ! [X2,X3] :
          ( ( X1 = X3
            & X0 = X2 )
          | rel_str_of(X0,X1) != rel_str_of(X2,X3) )
      | ~ relation_of2(X1,X0,X0) ),
    inference(ennf_transformation,[],[f46]) ).

fof(f128,plain,
    ! [X0,X1,X2] :
      ( ( below_refl(X0,X1,X2)
      <=> below(X0,X1,X2) )
      | ~ element(X2,the_carrier(X0))
      | ~ element(X1,the_carrier(X0))
      | ~ latt_str(X0)
      | ~ join_absorbing(X0)
      | ~ meet_absorbing(X0)
      | ~ meet_commutative(X0)
      | empty_carrier(X0) ),
    inference(ennf_transformation,[],[f57]) ).

fof(f129,plain,
    ! [X0,X1,X2] :
      ( ( below_refl(X0,X1,X2)
      <=> below(X0,X1,X2) )
      | ~ element(X2,the_carrier(X0))
      | ~ element(X1,the_carrier(X0))
      | ~ latt_str(X0)
      | ~ join_absorbing(X0)
      | ~ meet_absorbing(X0)
      | ~ meet_commutative(X0)
      | empty_carrier(X0) ),
    inference(flattening,[],[f128]) ).

fof(f130,plain,
    ! [X0,X1,X2] :
      ( ( related_reflexive(X0,X1,X2)
      <=> related(X0,X1,X2) )
      | ~ element(X2,the_carrier(X0))
      | ~ element(X1,the_carrier(X0))
      | ~ rel_str(X0)
      | ~ reflexive_relstr(X0)
      | empty_carrier(X0) ),
    inference(ennf_transformation,[],[f58]) ).

fof(f131,plain,
    ! [X0,X1,X2] :
      ( ( related_reflexive(X0,X1,X2)
      <=> related(X0,X1,X2) )
      | ~ element(X2,the_carrier(X0))
      | ~ element(X1,the_carrier(X0))
      | ~ rel_str(X0)
      | ~ reflexive_relstr(X0)
      | empty_carrier(X0) ),
    inference(flattening,[],[f130]) ).

fof(f137,plain,
    ? [X0,X1] :
      ( ? [X2] :
          ( ( 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)) )
      & latt_str(X1)
      & lattice(X1)
      & ~ empty_carrier(X1) ),
    inference(ennf_transformation,[],[f64]) ).

fof(f138,plain,
    ? [X0,X1] :
      ( ? [X2] :
          ( ( 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)) )
      & latt_str(X1)
      & lattice(X1)
      & ~ empty_carrier(X1) ),
    inference(flattening,[],[f137]) ).

fof(f147,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( below_refl(X0,X1,X2)
              <=> related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2)) )
              | ~ element(X2,the_carrier(X0)) )
          | ~ element(X1,the_carrier(X0)) )
      | ~ latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(ennf_transformation,[],[f71]) ).

fof(f148,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( below_refl(X0,X1,X2)
              <=> related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2)) )
              | ~ element(X2,the_carrier(X0)) )
          | ~ element(X1,the_carrier(X0)) )
      | ~ latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(flattening,[],[f147]) ).

fof(f150,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( latt_set_smaller(X0,X1,X2)
                | ? [X3] :
                    ( ~ below(X0,X1,X3)
                    & in(X3,X2)
                    & element(X3,the_carrier(X0)) ) )
              & ( ! [X3] :
                    ( below(X0,X1,X3)
                    | ~ in(X3,X2)
                    | ~ element(X3,the_carrier(X0)) )
                | ~ latt_set_smaller(X0,X1,X2) ) )
          | ~ element(X1,the_carrier(X0)) )
      | ~ latt_str(X0)
      | empty_carrier(X0) ),
    inference(nnf_transformation,[],[f86]) ).

fof(f151,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( latt_set_smaller(X0,X1,X2)
                | ? [X3] :
                    ( ~ below(X0,X1,X3)
                    & in(X3,X2)
                    & element(X3,the_carrier(X0)) ) )
              & ( ! [X4] :
                    ( below(X0,X1,X4)
                    | ~ in(X4,X2)
                    | ~ element(X4,the_carrier(X0)) )
                | ~ latt_set_smaller(X0,X1,X2) ) )
          | ~ element(X1,the_carrier(X0)) )
      | ~ latt_str(X0)
      | empty_carrier(X0) ),
    inference(rectify,[],[f150]) ).

fof(f152,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ~ below(X0,X1,X3)
          & in(X3,X2)
          & element(X3,the_carrier(X0)) )
     => ( ~ below(X0,X1,sK0(X0,X1,X2))
        & in(sK0(X0,X1,X2),X2)
        & element(sK0(X0,X1,X2),the_carrier(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f153,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( latt_set_smaller(X0,X1,X2)
                | ( ~ below(X0,X1,sK0(X0,X1,X2))
                  & in(sK0(X0,X1,X2),X2)
                  & element(sK0(X0,X1,X2),the_carrier(X0)) ) )
              & ( ! [X4] :
                    ( below(X0,X1,X4)
                    | ~ in(X4,X2)
                    | ~ element(X4,the_carrier(X0)) )
                | ~ latt_set_smaller(X0,X1,X2) ) )
          | ~ element(X1,the_carrier(X0)) )
      | ~ latt_str(X0)
      | empty_carrier(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f151,f152]) ).

fof(f154,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( ( relstr_element_smaller(X0,X1,X2)
              | ? [X3] :
                  ( ~ related(X0,X2,X3)
                  & in(X3,X1)
                  & element(X3,the_carrier(X0)) ) )
            & ( ! [X3] :
                  ( related(X0,X2,X3)
                  | ~ in(X3,X1)
                  | ~ element(X3,the_carrier(X0)) )
              | ~ relstr_element_smaller(X0,X1,X2) ) )
          | ~ element(X2,the_carrier(X0)) )
      | ~ rel_str(X0) ),
    inference(nnf_transformation,[],[f94]) ).

fof(f155,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( ( relstr_element_smaller(X0,X1,X2)
              | ? [X3] :
                  ( ~ related(X0,X2,X3)
                  & in(X3,X1)
                  & element(X3,the_carrier(X0)) ) )
            & ( ! [X4] :
                  ( related(X0,X2,X4)
                  | ~ in(X4,X1)
                  | ~ element(X4,the_carrier(X0)) )
              | ~ relstr_element_smaller(X0,X1,X2) ) )
          | ~ element(X2,the_carrier(X0)) )
      | ~ rel_str(X0) ),
    inference(rectify,[],[f154]) ).

fof(f156,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ~ related(X0,X2,X3)
          & in(X3,X1)
          & element(X3,the_carrier(X0)) )
     => ( ~ related(X0,X2,sK1(X0,X1,X2))
        & in(sK1(X0,X1,X2),X1)
        & element(sK1(X0,X1,X2),the_carrier(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f157,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( ( relstr_element_smaller(X0,X1,X2)
              | ( ~ related(X0,X2,sK1(X0,X1,X2))
                & in(sK1(X0,X1,X2),X1)
                & element(sK1(X0,X1,X2),the_carrier(X0)) ) )
            & ( ! [X4] :
                  ( related(X0,X2,X4)
                  | ~ in(X4,X1)
                  | ~ element(X4,the_carrier(X0)) )
              | ~ relstr_element_smaller(X0,X1,X2) ) )
          | ~ element(X2,the_carrier(X0)) )
      | ~ rel_str(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f155,f156]) ).

fof(f190,plain,
    ! [X0,X1,X2] :
      ( ( relation_of2_as_subset(X2,X0,X1)
        | ~ relation_of2(X2,X0,X1) )
      & ( relation_of2(X2,X0,X1)
        | ~ relation_of2_as_subset(X2,X0,X1) ) ),
    inference(nnf_transformation,[],[f56]) ).

fof(f191,plain,
    ! [X0,X1,X2] :
      ( ( ( below_refl(X0,X1,X2)
          | ~ below(X0,X1,X2) )
        & ( below(X0,X1,X2)
          | ~ below_refl(X0,X1,X2) ) )
      | ~ element(X2,the_carrier(X0))
      | ~ element(X1,the_carrier(X0))
      | ~ latt_str(X0)
      | ~ join_absorbing(X0)
      | ~ meet_absorbing(X0)
      | ~ meet_commutative(X0)
      | empty_carrier(X0) ),
    inference(nnf_transformation,[],[f129]) ).

fof(f192,plain,
    ! [X0,X1,X2] :
      ( ( ( related_reflexive(X0,X1,X2)
          | ~ related(X0,X1,X2) )
        & ( related(X0,X1,X2)
          | ~ related_reflexive(X0,X1,X2) ) )
      | ~ element(X2,the_carrier(X0))
      | ~ element(X1,the_carrier(X0))
      | ~ rel_str(X0)
      | ~ reflexive_relstr(X0)
      | empty_carrier(X0) ),
    inference(nnf_transformation,[],[f131]) ).

fof(f193,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) )
          & ( 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)
      & lattice(X1)
      & ~ empty_carrier(X1) ),
    inference(nnf_transformation,[],[f138]) ).

fof(f194,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) )
          & ( 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)
      & lattice(X1)
      & ~ empty_carrier(X1) ),
    inference(flattening,[],[f193]) ).

fof(f195,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) )
            & ( 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)
        & lattice(X1)
        & ~ empty_carrier(X1) )
   => ( ? [X2] :
          ( ( ~ relstr_element_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,X2))
            | ~ latt_set_smaller(sK19,X2,sK18) )
          & ( relstr_element_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,X2))
            | latt_set_smaller(sK19,X2,sK18) )
          & element(X2,the_carrier(sK19)) )
      & latt_str(sK19)
      & lattice(sK19)
      & ~ empty_carrier(sK19) ) ),
    introduced(choice_axiom,[]) ).

fof(f196,plain,
    ( ? [X2] :
        ( ( ~ relstr_element_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,X2))
          | ~ latt_set_smaller(sK19,X2,sK18) )
        & ( relstr_element_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,X2))
          | latt_set_smaller(sK19,X2,sK18) )
        & element(X2,the_carrier(sK19)) )
   => ( ( ~ relstr_element_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
        | ~ latt_set_smaller(sK19,sK20,sK18) )
      & ( relstr_element_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
        | latt_set_smaller(sK19,sK20,sK18) )
      & element(sK20,the_carrier(sK19)) ) ),
    introduced(choice_axiom,[]) ).

fof(f197,plain,
    ( ( ~ relstr_element_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
      | ~ latt_set_smaller(sK19,sK20,sK18) )
    & ( relstr_element_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
      | latt_set_smaller(sK19,sK20,sK18) )
    & element(sK20,the_carrier(sK19))
    & latt_str(sK19)
    & lattice(sK19)
    & ~ empty_carrier(sK19) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20])],[f194,f196,f195]) ).

fof(f198,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( below_refl(X0,X1,X2)
                  | ~ related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2)) )
                & ( related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2))
                  | ~ below_refl(X0,X1,X2) ) )
              | ~ element(X2,the_carrier(X0)) )
          | ~ element(X1,the_carrier(X0)) )
      | ~ latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(nnf_transformation,[],[f148]) ).

fof(f199,plain,
    ! [X0] :
      ( rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
      | ~ strict_rel_str(X0)
      | ~ rel_str(X0) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f204,plain,
    ! [X0] :
      ( meet_commutative(X0)
      | ~ lattice(X0)
      | empty_carrier(X0)
      | ~ latt_str(X0) ),
    inference(cnf_transformation,[],[f82]) ).

fof(f206,plain,
    ! [X0] :
      ( meet_absorbing(X0)
      | ~ lattice(X0)
      | empty_carrier(X0)
      | ~ latt_str(X0) ),
    inference(cnf_transformation,[],[f82]) ).

fof(f207,plain,
    ! [X0] :
      ( join_absorbing(X0)
      | ~ lattice(X0)
      | empty_carrier(X0)
      | ~ latt_str(X0) ),
    inference(cnf_transformation,[],[f82]) ).

fof(f210,plain,
    ! [X2,X0,X1,X4] :
      ( below(X0,X1,X4)
      | ~ in(X4,X2)
      | ~ element(X4,the_carrier(X0))
      | ~ latt_set_smaller(X0,X1,X2)
      | ~ element(X1,the_carrier(X0))
      | ~ latt_str(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f153]) ).

fof(f211,plain,
    ! [X2,X0,X1] :
      ( latt_set_smaller(X0,X1,X2)
      | element(sK0(X0,X1,X2),the_carrier(X0))
      | ~ element(X1,the_carrier(X0))
      | ~ latt_str(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f153]) ).

fof(f212,plain,
    ! [X2,X0,X1] :
      ( latt_set_smaller(X0,X1,X2)
      | in(sK0(X0,X1,X2),X2)
      | ~ element(X1,the_carrier(X0))
      | ~ latt_str(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f153]) ).

fof(f213,plain,
    ! [X2,X0,X1] :
      ( latt_set_smaller(X0,X1,X2)
      | ~ below(X0,X1,sK0(X0,X1,X2))
      | ~ element(X1,the_carrier(X0))
      | ~ latt_str(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f153]) ).

fof(f214,plain,
    ! [X0] :
      ( poset_of_lattice(X0) = rel_str_of(the_carrier(X0),k2_lattice3(X0))
      | ~ latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f215,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,[],[f90]) ).

fof(f217,plain,
    ! [X2,X0,X1,X4] :
      ( related(X0,X2,X4)
      | ~ in(X4,X1)
      | ~ element(X4,the_carrier(X0))
      | ~ relstr_element_smaller(X0,X1,X2)
      | ~ element(X2,the_carrier(X0))
      | ~ rel_str(X0) ),
    inference(cnf_transformation,[],[f157]) ).

fof(f218,plain,
    ! [X2,X0,X1] :
      ( relstr_element_smaller(X0,X1,X2)
      | element(sK1(X0,X1,X2),the_carrier(X0))
      | ~ element(X2,the_carrier(X0))
      | ~ rel_str(X0) ),
    inference(cnf_transformation,[],[f157]) ).

fof(f219,plain,
    ! [X2,X0,X1] :
      ( relstr_element_smaller(X0,X1,X2)
      | in(sK1(X0,X1,X2),X1)
      | ~ element(X2,the_carrier(X0))
      | ~ rel_str(X0) ),
    inference(cnf_transformation,[],[f157]) ).

fof(f220,plain,
    ! [X2,X0,X1] :
      ( relstr_element_smaller(X0,X1,X2)
      | ~ related(X0,X2,sK1(X0,X1,X2))
      | ~ element(X2,the_carrier(X0))
      | ~ rel_str(X0) ),
    inference(cnf_transformation,[],[f157]) ).

fof(f227,plain,
    ! [X0] :
      ( relation_of2_as_subset(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
      | ~ latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f97]) ).

fof(f232,plain,
    ! [X0] :
      ( rel_str(poset_of_lattice(X0))
      | ~ latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f233,plain,
    ! [X0,X1] :
      ( element(cast_to_el_of_LattPOSet(X0,X1),the_carrier(poset_of_lattice(X0)))
      | ~ element(X1,the_carrier(X0))
      | ~ latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f101]) ).

fof(f263,plain,
    ! [X0] :
      ( ~ empty_carrier(poset_of_lattice(X0))
      | ~ latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f119]) ).

fof(f264,plain,
    ! [X0] :
      ( strict_rel_str(poset_of_lattice(X0))
      | ~ latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f119]) ).

fof(f265,plain,
    ! [X0] :
      ( reflexive_relstr(poset_of_lattice(X0))
      | ~ latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f119]) ).

fof(f269,plain,
    ! [X2,X3,X0,X1] :
      ( X0 = X2
      | rel_str_of(X0,X1) != rel_str_of(X2,X3)
      | ~ relation_of2(X1,X0,X0) ),
    inference(cnf_transformation,[],[f122]) ).

fof(f290,plain,
    ! [X2,X0,X1] :
      ( relation_of2(X2,X0,X1)
      | ~ relation_of2_as_subset(X2,X0,X1) ),
    inference(cnf_transformation,[],[f190]) ).

fof(f292,plain,
    ! [X2,X0,X1] :
      ( below(X0,X1,X2)
      | ~ below_refl(X0,X1,X2)
      | ~ element(X2,the_carrier(X0))
      | ~ element(X1,the_carrier(X0))
      | ~ latt_str(X0)
      | ~ join_absorbing(X0)
      | ~ meet_absorbing(X0)
      | ~ meet_commutative(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f191]) ).

fof(f293,plain,
    ! [X2,X0,X1] :
      ( below_refl(X0,X1,X2)
      | ~ below(X0,X1,X2)
      | ~ element(X2,the_carrier(X0))
      | ~ element(X1,the_carrier(X0))
      | ~ latt_str(X0)
      | ~ join_absorbing(X0)
      | ~ meet_absorbing(X0)
      | ~ meet_commutative(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f191]) ).

fof(f294,plain,
    ! [X2,X0,X1] :
      ( related(X0,X1,X2)
      | ~ related_reflexive(X0,X1,X2)
      | ~ element(X2,the_carrier(X0))
      | ~ element(X1,the_carrier(X0))
      | ~ rel_str(X0)
      | ~ reflexive_relstr(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f192]) ).

fof(f295,plain,
    ! [X2,X0,X1] :
      ( related_reflexive(X0,X1,X2)
      | ~ related(X0,X1,X2)
      | ~ element(X2,the_carrier(X0))
      | ~ element(X1,the_carrier(X0))
      | ~ rel_str(X0)
      | ~ reflexive_relstr(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f192]) ).

fof(f300,plain,
    ~ empty_carrier(sK19),
    inference(cnf_transformation,[],[f197]) ).

fof(f301,plain,
    lattice(sK19),
    inference(cnf_transformation,[],[f197]) ).

fof(f302,plain,
    latt_str(sK19),
    inference(cnf_transformation,[],[f197]) ).

fof(f303,plain,
    element(sK20,the_carrier(sK19)),
    inference(cnf_transformation,[],[f197]) ).

fof(f304,plain,
    ( relstr_element_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
    | latt_set_smaller(sK19,sK20,sK18) ),
    inference(cnf_transformation,[],[f197]) ).

fof(f305,plain,
    ( ~ relstr_element_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
    | ~ latt_set_smaller(sK19,sK20,sK18) ),
    inference(cnf_transformation,[],[f197]) ).

fof(f312,plain,
    ! [X2,X0,X1] :
      ( related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2))
      | ~ below_refl(X0,X1,X2)
      | ~ element(X2,the_carrier(X0))
      | ~ element(X1,the_carrier(X0))
      | ~ latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f198]) ).

fof(f313,plain,
    ! [X2,X0,X1] :
      ( below_refl(X0,X1,X2)
      | ~ related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2))
      | ~ element(X2,the_carrier(X0))
      | ~ element(X1,the_carrier(X0))
      | ~ latt_str(X0)
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f198]) ).

cnf(c_49,plain,
    ( ~ strict_rel_str(X0)
    | ~ rel_str(X0)
    | rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0 ),
    inference(cnf_transformation,[],[f199]) ).

cnf(c_51,plain,
    ( ~ lattice(X0)
    | ~ latt_str(X0)
    | join_absorbing(X0)
    | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f207]) ).

cnf(c_52,plain,
    ( ~ lattice(X0)
    | ~ latt_str(X0)
    | empty_carrier(X0)
    | meet_absorbing(X0) ),
    inference(cnf_transformation,[],[f206]) ).

cnf(c_54,plain,
    ( ~ lattice(X0)
    | ~ latt_str(X0)
    | empty_carrier(X0)
    | meet_commutative(X0) ),
    inference(cnf_transformation,[],[f204]) ).

cnf(c_58,plain,
    ( ~ below(X0,X1,sK0(X0,X1,X2))
    | ~ element(X1,the_carrier(X0))
    | ~ latt_str(X0)
    | latt_set_smaller(X0,X1,X2)
    | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f213]) ).

cnf(c_59,plain,
    ( ~ element(X0,the_carrier(X1))
    | ~ latt_str(X1)
    | in(sK0(X1,X0,X2),X2)
    | latt_set_smaller(X1,X0,X2)
    | empty_carrier(X1) ),
    inference(cnf_transformation,[],[f212]) ).

cnf(c_60,plain,
    ( ~ element(X0,the_carrier(X1))
    | ~ latt_str(X1)
    | element(sK0(X1,X0,X2),the_carrier(X1))
    | latt_set_smaller(X1,X0,X2)
    | empty_carrier(X1) ),
    inference(cnf_transformation,[],[f211]) ).

cnf(c_61,plain,
    ( ~ latt_set_smaller(X0,X1,X2)
    | ~ element(X1,the_carrier(X0))
    | ~ element(X3,the_carrier(X0))
    | ~ in(X3,X2)
    | ~ latt_str(X0)
    | below(X0,X1,X3)
    | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f210]) ).

cnf(c_62,plain,
    ( ~ lattice(X0)
    | ~ latt_str(X0)
    | rel_str_of(the_carrier(X0),k2_lattice3(X0)) = poset_of_lattice(X0)
    | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f214]) ).

cnf(c_63,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,[],[f215]) ).

cnf(c_65,plain,
    ( ~ related(X0,X1,sK1(X0,X2,X1))
    | ~ element(X1,the_carrier(X0))
    | ~ rel_str(X0)
    | relstr_element_smaller(X0,X2,X1) ),
    inference(cnf_transformation,[],[f220]) ).

cnf(c_66,plain,
    ( ~ element(X0,the_carrier(X1))
    | ~ rel_str(X1)
    | in(sK1(X1,X2,X0),X2)
    | relstr_element_smaller(X1,X2,X0) ),
    inference(cnf_transformation,[],[f219]) ).

cnf(c_67,plain,
    ( ~ element(X0,the_carrier(X1))
    | ~ rel_str(X1)
    | element(sK1(X1,X2,X0),the_carrier(X1))
    | relstr_element_smaller(X1,X2,X0) ),
    inference(cnf_transformation,[],[f218]) ).

cnf(c_68,plain,
    ( ~ relstr_element_smaller(X0,X1,X2)
    | ~ element(X2,the_carrier(X0))
    | ~ element(X3,the_carrier(X0))
    | ~ in(X3,X1)
    | ~ rel_str(X0)
    | related(X0,X2,X3) ),
    inference(cnf_transformation,[],[f217]) ).

cnf(c_71,plain,
    ( ~ lattice(X0)
    | ~ latt_str(X0)
    | relation_of2_as_subset(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
    | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f227]) ).

cnf(c_76,plain,
    ( ~ lattice(X0)
    | ~ latt_str(X0)
    | rel_str(poset_of_lattice(X0))
    | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f232]) ).

cnf(c_81,plain,
    ( ~ element(X0,the_carrier(X1))
    | ~ lattice(X1)
    | ~ latt_str(X1)
    | element(cast_to_el_of_LattPOSet(X1,X0),the_carrier(poset_of_lattice(X1)))
    | empty_carrier(X1) ),
    inference(cnf_transformation,[],[f233]) ).

cnf(c_113,plain,
    ( ~ lattice(X0)
    | ~ latt_str(X0)
    | reflexive_relstr(poset_of_lattice(X0))
    | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f265]) ).

cnf(c_114,plain,
    ( ~ lattice(X0)
    | ~ latt_str(X0)
    | strict_rel_str(poset_of_lattice(X0))
    | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f264]) ).

cnf(c_115,plain,
    ( ~ empty_carrier(poset_of_lattice(X0))
    | ~ lattice(X0)
    | ~ latt_str(X0)
    | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f263]) ).

cnf(c_118,plain,
    ( rel_str_of(X0,X1) != rel_str_of(X2,X3)
    | ~ relation_of2(X1,X0,X0)
    | X0 = X2 ),
    inference(cnf_transformation,[],[f269]) ).

cnf(c_139,plain,
    ( ~ relation_of2_as_subset(X0,X1,X2)
    | relation_of2(X0,X1,X2) ),
    inference(cnf_transformation,[],[f290]) ).

cnf(c_140,plain,
    ( ~ below(X0,X1,X2)
    | ~ element(X1,the_carrier(X0))
    | ~ element(X2,the_carrier(X0))
    | ~ join_absorbing(X0)
    | ~ latt_str(X0)
    | ~ meet_absorbing(X0)
    | ~ meet_commutative(X0)
    | below_refl(X0,X1,X2)
    | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f293]) ).

cnf(c_141,plain,
    ( ~ below_refl(X0,X1,X2)
    | ~ element(X1,the_carrier(X0))
    | ~ element(X2,the_carrier(X0))
    | ~ join_absorbing(X0)
    | ~ latt_str(X0)
    | ~ meet_absorbing(X0)
    | ~ meet_commutative(X0)
    | below(X0,X1,X2)
    | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f292]) ).

cnf(c_142,plain,
    ( ~ related(X0,X1,X2)
    | ~ element(X1,the_carrier(X0))
    | ~ element(X2,the_carrier(X0))
    | ~ rel_str(X0)
    | ~ reflexive_relstr(X0)
    | related_reflexive(X0,X1,X2)
    | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f295]) ).

cnf(c_143,plain,
    ( ~ related_reflexive(X0,X1,X2)
    | ~ element(X1,the_carrier(X0))
    | ~ element(X2,the_carrier(X0))
    | ~ rel_str(X0)
    | ~ reflexive_relstr(X0)
    | related(X0,X1,X2)
    | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f294]) ).

cnf(c_148,negated_conjecture,
    ( ~ relstr_element_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
    | ~ latt_set_smaller(sK19,sK20,sK18) ),
    inference(cnf_transformation,[],[f305]) ).

cnf(c_149,negated_conjecture,
    ( relstr_element_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
    | latt_set_smaller(sK19,sK20,sK18) ),
    inference(cnf_transformation,[],[f304]) ).

cnf(c_150,negated_conjecture,
    element(sK20,the_carrier(sK19)),
    inference(cnf_transformation,[],[f303]) ).

cnf(c_151,negated_conjecture,
    latt_str(sK19),
    inference(cnf_transformation,[],[f302]) ).

cnf(c_152,negated_conjecture,
    lattice(sK19),
    inference(cnf_transformation,[],[f301]) ).

cnf(c_153,negated_conjecture,
    ~ empty_carrier(sK19),
    inference(cnf_transformation,[],[f300]) ).

cnf(c_160,plain,
    ( ~ related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2))
    | ~ element(X1,the_carrier(X0))
    | ~ element(X2,the_carrier(X0))
    | ~ lattice(X0)
    | ~ latt_str(X0)
    | below_refl(X0,X1,X2)
    | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f313]) ).

cnf(c_161,plain,
    ( ~ below_refl(X0,X1,X2)
    | ~ element(X1,the_carrier(X0))
    | ~ element(X2,the_carrier(X0))
    | ~ lattice(X0)
    | ~ latt_str(X0)
    | related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2))
    | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f312]) ).

cnf(c_199,plain,
    ( ~ lattice(sK19)
    | ~ latt_str(sK19)
    | strict_rel_str(poset_of_lattice(sK19))
    | empty_carrier(sK19) ),
    inference(instantiation,[status(thm)],[c_114]) ).

cnf(c_200,plain,
    ( ~ lattice(sK19)
    | ~ latt_str(sK19)
    | reflexive_relstr(poset_of_lattice(sK19))
    | empty_carrier(sK19) ),
    inference(instantiation,[status(thm)],[c_113]) ).

cnf(c_204,plain,
    ( ~ lattice(sK19)
    | ~ latt_str(sK19)
    | rel_str(poset_of_lattice(sK19))
    | empty_carrier(sK19) ),
    inference(instantiation,[status(thm)],[c_76]) ).

cnf(c_208,plain,
    ( ~ empty_carrier(poset_of_lattice(sK19))
    | ~ lattice(sK19)
    | ~ latt_str(sK19)
    | empty_carrier(sK19) ),
    inference(instantiation,[status(thm)],[c_115]) ).

cnf(c_217,plain,
    ( ~ lattice(sK19)
    | ~ latt_str(sK19)
    | rel_str_of(the_carrier(sK19),k2_lattice3(sK19)) = poset_of_lattice(sK19)
    | empty_carrier(sK19) ),
    inference(instantiation,[status(thm)],[c_62]) ).

cnf(c_245,plain,
    ( ~ relation_of2_as_subset(X0,X1,X2)
    | relation_of2(X0,X1,X2) ),
    inference(prop_impl_just,[status(thm)],[c_139]) ).

cnf(c_1312,plain,
    ( the_carrier(X0) != X1
    | the_carrier(X0) != X2
    | k2_lattice3(X0) != X3
    | ~ lattice(X0)
    | ~ latt_str(X0)
    | relation_of2(X3,X1,X2)
    | empty_carrier(X0) ),
    inference(resolution_lifted,[status(thm)],[c_71,c_245]) ).

cnf(c_1313,plain,
    ( ~ lattice(X0)
    | ~ latt_str(X0)
    | relation_of2(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
    | empty_carrier(X0) ),
    inference(unflattening,[status(thm)],[c_1312]) ).

cnf(c_1314,plain,
    ( ~ lattice(sK19)
    | ~ latt_str(sK19)
    | relation_of2(k2_lattice3(sK19),the_carrier(sK19),the_carrier(sK19))
    | empty_carrier(sK19) ),
    inference(instantiation,[status(thm)],[c_1313]) ).

cnf(c_1388,plain,
    ( X0 != X1
    | ~ below_refl(X1,X2,X3)
    | ~ element(X2,the_carrier(X1))
    | ~ element(X3,the_carrier(X1))
    | ~ lattice(X0)
    | ~ latt_str(X0)
    | ~ latt_str(X1)
    | ~ meet_absorbing(X1)
    | ~ meet_commutative(X1)
    | below(X1,X2,X3)
    | empty_carrier(X0)
    | empty_carrier(X1) ),
    inference(resolution_lifted,[status(thm)],[c_51,c_141]) ).

cnf(c_1389,plain,
    ( ~ below_refl(X0,X1,X2)
    | ~ element(X1,the_carrier(X0))
    | ~ element(X2,the_carrier(X0))
    | ~ lattice(X0)
    | ~ latt_str(X0)
    | ~ meet_absorbing(X0)
    | ~ meet_commutative(X0)
    | below(X0,X1,X2)
    | empty_carrier(X0) ),
    inference(unflattening,[status(thm)],[c_1388]) ).

cnf(c_1391,plain,
    ( ~ below_refl(X0,X1,X2)
    | ~ element(X1,the_carrier(X0))
    | ~ element(X2,the_carrier(X0))
    | ~ lattice(X0)
    | ~ latt_str(X0)
    | below(X0,X1,X2)
    | empty_carrier(X0) ),
    inference(global_subsumption_just,[status(thm)],[c_1389,c_54,c_52,c_1389]) ).

cnf(c_1415,plain,
    ( X0 != X1
    | ~ below(X1,X2,X3)
    | ~ element(X2,the_carrier(X1))
    | ~ element(X3,the_carrier(X1))
    | ~ lattice(X0)
    | ~ latt_str(X0)
    | ~ latt_str(X1)
    | ~ meet_absorbing(X1)
    | ~ meet_commutative(X1)
    | below_refl(X1,X2,X3)
    | empty_carrier(X0)
    | empty_carrier(X1) ),
    inference(resolution_lifted,[status(thm)],[c_51,c_140]) ).

cnf(c_1416,plain,
    ( ~ below(X0,X1,X2)
    | ~ element(X1,the_carrier(X0))
    | ~ element(X2,the_carrier(X0))
    | ~ lattice(X0)
    | ~ latt_str(X0)
    | ~ meet_absorbing(X0)
    | ~ meet_commutative(X0)
    | below_refl(X0,X1,X2)
    | empty_carrier(X0) ),
    inference(unflattening,[status(thm)],[c_1415]) ).

cnf(c_1418,plain,
    ( ~ below(X0,X1,X2)
    | ~ element(X1,the_carrier(X0))
    | ~ element(X2,the_carrier(X0))
    | ~ lattice(X0)
    | ~ latt_str(X0)
    | below_refl(X0,X1,X2)
    | empty_carrier(X0) ),
    inference(global_subsumption_just,[status(thm)],[c_1416,c_54,c_52,c_51,c_140]) ).

cnf(c_1511,plain,
    ( sK1(X0,X1,X2) != X3
    | X0 != X4
    | X2 != X5
    | ~ related_reflexive(X4,X5,X3)
    | ~ element(X2,the_carrier(X0))
    | ~ element(X3,the_carrier(X4))
    | ~ element(X5,the_carrier(X4))
    | ~ rel_str(X0)
    | ~ rel_str(X4)
    | ~ reflexive_relstr(X4)
    | relstr_element_smaller(X0,X1,X2)
    | empty_carrier(X4) ),
    inference(resolution_lifted,[status(thm)],[c_65,c_143]) ).

cnf(c_1512,plain,
    ( ~ related_reflexive(X0,X1,sK1(X0,X2,X1))
    | ~ element(sK1(X0,X2,X1),the_carrier(X0))
    | ~ element(X1,the_carrier(X0))
    | ~ rel_str(X0)
    | ~ reflexive_relstr(X0)
    | relstr_element_smaller(X0,X2,X1)
    | empty_carrier(X0) ),
    inference(unflattening,[status(thm)],[c_1511]) ).

cnf(c_1528,plain,
    ( ~ related_reflexive(X0,X1,sK1(X0,X2,X1))
    | ~ element(X1,the_carrier(X0))
    | ~ rel_str(X0)
    | ~ reflexive_relstr(X0)
    | relstr_element_smaller(X0,X2,X1)
    | empty_carrier(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_1512,c_67]) ).

cnf(c_1536,plain,
    ( X0 != X1
    | X2 != X3
    | X4 != X5
    | ~ relstr_element_smaller(X0,X6,X2)
    | ~ element(X2,the_carrier(X0))
    | ~ element(X3,the_carrier(X1))
    | ~ element(X4,the_carrier(X0))
    | ~ element(X5,the_carrier(X1))
    | ~ in(X4,X6)
    | ~ rel_str(X0)
    | ~ rel_str(X1)
    | ~ reflexive_relstr(X1)
    | related_reflexive(X1,X3,X5)
    | empty_carrier(X1) ),
    inference(resolution_lifted,[status(thm)],[c_68,c_142]) ).

cnf(c_1537,plain,
    ( ~ relstr_element_smaller(X0,X1,X2)
    | ~ element(X2,the_carrier(X0))
    | ~ element(X3,the_carrier(X0))
    | ~ in(X3,X1)
    | ~ rel_str(X0)
    | ~ reflexive_relstr(X0)
    | related_reflexive(X0,X2,X3)
    | empty_carrier(X0) ),
    inference(unflattening,[status(thm)],[c_1536]) ).

cnf(c_1810,plain,
    ( sK0(X0,X1,X2) != X3
    | X0 != X4
    | X1 != X5
    | ~ below_refl(X4,X5,X3)
    | ~ element(X1,the_carrier(X0))
    | ~ element(X3,the_carrier(X4))
    | ~ element(X5,the_carrier(X4))
    | ~ lattice(X4)
    | ~ latt_str(X0)
    | ~ latt_str(X4)
    | latt_set_smaller(X0,X1,X2)
    | empty_carrier(X0)
    | empty_carrier(X4) ),
    inference(resolution_lifted,[status(thm)],[c_58,c_1391]) ).

cnf(c_1811,plain,
    ( ~ below_refl(X0,X1,sK0(X0,X1,X2))
    | ~ element(sK0(X0,X1,X2),the_carrier(X0))
    | ~ element(X1,the_carrier(X0))
    | ~ lattice(X0)
    | ~ latt_str(X0)
    | latt_set_smaller(X0,X1,X2)
    | empty_carrier(X0) ),
    inference(unflattening,[status(thm)],[c_1810]) ).

cnf(c_1827,plain,
    ( ~ below_refl(X0,X1,sK0(X0,X1,X2))
    | ~ element(X1,the_carrier(X0))
    | ~ lattice(X0)
    | ~ latt_str(X0)
    | latt_set_smaller(X0,X1,X2)
    | empty_carrier(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_1811,c_60]) ).

cnf(c_1835,plain,
    ( X0 != X1
    | X2 != X3
    | X4 != X5
    | ~ latt_set_smaller(X0,X2,X6)
    | ~ element(X2,the_carrier(X0))
    | ~ element(X3,the_carrier(X1))
    | ~ element(X4,the_carrier(X0))
    | ~ element(X5,the_carrier(X1))
    | ~ in(X4,X6)
    | ~ lattice(X1)
    | ~ latt_str(X0)
    | ~ latt_str(X1)
    | below_refl(X1,X3,X5)
    | empty_carrier(X0)
    | empty_carrier(X1) ),
    inference(resolution_lifted,[status(thm)],[c_61,c_1418]) ).

cnf(c_1836,plain,
    ( ~ latt_set_smaller(X0,X1,X2)
    | ~ element(X1,the_carrier(X0))
    | ~ element(X3,the_carrier(X0))
    | ~ in(X3,X2)
    | ~ lattice(X0)
    | ~ latt_str(X0)
    | below_refl(X0,X1,X3)
    | empty_carrier(X0) ),
    inference(unflattening,[status(thm)],[c_1835]) ).

cnf(c_2328,plain,
    ( sK0(X1,X3,X4) != X5
    | X0 != X1
    | X2 != X3
    | ~ related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X2),cast_to_el_of_LattPOSet(X0,X5))
    | ~ element(X2,the_carrier(X0))
    | ~ element(X3,the_carrier(X1))
    | ~ element(X5,the_carrier(X0))
    | ~ lattice(X0)
    | ~ lattice(X1)
    | ~ latt_str(X0)
    | ~ latt_str(X1)
    | latt_set_smaller(X1,X3,X4)
    | empty_carrier(X0)
    | empty_carrier(X1) ),
    inference(resolution_lifted,[status(thm)],[c_160,c_1827]) ).

cnf(c_2329,plain,
    ( ~ related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,sK0(X0,X1,X2)))
    | ~ element(sK0(X0,X1,X2),the_carrier(X0))
    | ~ element(X1,the_carrier(X0))
    | ~ lattice(X0)
    | ~ latt_str(X0)
    | latt_set_smaller(X0,X1,X2)
    | empty_carrier(X0) ),
    inference(unflattening,[status(thm)],[c_2328]) ).

cnf(c_2345,plain,
    ( ~ related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,sK0(X0,X1,X2)))
    | ~ element(X1,the_carrier(X0))
    | ~ lattice(X0)
    | ~ latt_str(X0)
    | latt_set_smaller(X0,X1,X2)
    | empty_carrier(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_2329,c_60]) ).

cnf(c_2353,plain,
    ( X0 != X1
    | X2 != X3
    | X4 != X5
    | ~ latt_set_smaller(X1,X3,X6)
    | ~ element(X2,the_carrier(X0))
    | ~ element(X3,the_carrier(X1))
    | ~ element(X4,the_carrier(X0))
    | ~ element(X5,the_carrier(X1))
    | ~ in(X5,X6)
    | ~ lattice(X0)
    | ~ lattice(X1)
    | ~ latt_str(X0)
    | ~ latt_str(X1)
    | related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X2),cast_to_el_of_LattPOSet(X0,X4))
    | empty_carrier(X0)
    | empty_carrier(X1) ),
    inference(resolution_lifted,[status(thm)],[c_161,c_1836]) ).

cnf(c_2354,plain,
    ( ~ latt_set_smaller(X0,X1,X2)
    | ~ element(X1,the_carrier(X0))
    | ~ element(X3,the_carrier(X0))
    | ~ in(X3,X2)
    | ~ lattice(X0)
    | ~ latt_str(X0)
    | related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X3))
    | empty_carrier(X0) ),
    inference(unflattening,[status(thm)],[c_2353]) ).

cnf(c_2452,plain,
    ( X0 != sK19
    | ~ latt_set_smaller(X0,X1,X2)
    | ~ element(X1,the_carrier(X0))
    | ~ element(X3,the_carrier(X0))
    | ~ in(X3,X2)
    | ~ latt_str(X0)
    | related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X3))
    | empty_carrier(X0) ),
    inference(resolution_lifted,[status(thm)],[c_2354,c_152]) ).

cnf(c_2453,plain,
    ( ~ latt_set_smaller(sK19,X0,X1)
    | ~ element(X0,the_carrier(sK19))
    | ~ element(X2,the_carrier(sK19))
    | ~ in(X2,X1)
    | ~ latt_str(sK19)
    | related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,X0),cast_to_el_of_LattPOSet(sK19,X2))
    | empty_carrier(sK19) ),
    inference(unflattening,[status(thm)],[c_2452]) ).

cnf(c_2454,plain,
    ( related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,X0),cast_to_el_of_LattPOSet(sK19,X2))
    | ~ latt_set_smaller(sK19,X0,X1)
    | ~ element(X0,the_carrier(sK19))
    | ~ element(X2,the_carrier(sK19))
    | ~ in(X2,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_2453,c_151,c_153,c_2453]) ).

cnf(c_2455,plain,
    ( ~ latt_set_smaller(sK19,X0,X1)
    | ~ element(X0,the_carrier(sK19))
    | ~ element(X2,the_carrier(sK19))
    | ~ in(X2,X1)
    | related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,X0),cast_to_el_of_LattPOSet(sK19,X2)) ),
    inference(renaming,[status(thm)],[c_2454]) ).

cnf(c_2471,plain,
    ( X0 != sK19
    | ~ related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,sK0(X0,X1,X2)))
    | ~ element(X1,the_carrier(X0))
    | ~ latt_str(X0)
    | latt_set_smaller(X0,X1,X2)
    | empty_carrier(X0) ),
    inference(resolution_lifted,[status(thm)],[c_2345,c_152]) ).

cnf(c_2472,plain,
    ( ~ related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,X0),cast_to_el_of_LattPOSet(sK19,sK0(sK19,X0,X1)))
    | ~ element(X0,the_carrier(sK19))
    | ~ latt_str(sK19)
    | latt_set_smaller(sK19,X0,X1)
    | empty_carrier(sK19) ),
    inference(unflattening,[status(thm)],[c_2471]) ).

cnf(c_2474,plain,
    ( latt_set_smaller(sK19,X0,X1)
    | ~ related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,X0),cast_to_el_of_LattPOSet(sK19,sK0(sK19,X0,X1)))
    | ~ element(X0,the_carrier(sK19)) ),
    inference(global_subsumption_just,[status(thm)],[c_2472,c_151,c_153,c_2472]) ).

cnf(c_2475,plain,
    ( ~ related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,X0),cast_to_el_of_LattPOSet(sK19,sK0(sK19,X0,X1)))
    | ~ element(X0,the_carrier(sK19))
    | latt_set_smaller(sK19,X0,X1) ),
    inference(renaming,[status(thm)],[c_2474]) ).

cnf(c_2570,plain,
    ( X0 != sK19
    | ~ latt_str(X0)
    | rel_str_of(the_carrier(X0),k2_lattice3(X0)) = poset_of_lattice(X0)
    | empty_carrier(X0) ),
    inference(resolution_lifted,[status(thm)],[c_62,c_152]) ).

cnf(c_2571,plain,
    ( ~ latt_str(sK19)
    | rel_str_of(the_carrier(sK19),k2_lattice3(sK19)) = poset_of_lattice(sK19)
    | empty_carrier(sK19) ),
    inference(unflattening,[status(thm)],[c_2570]) ).

cnf(c_2572,plain,
    rel_str_of(the_carrier(sK19),k2_lattice3(sK19)) = poset_of_lattice(sK19),
    inference(global_subsumption_just,[status(thm)],[c_2571,c_152,c_151,c_153,c_217]) ).

cnf(c_2604,plain,
    ( X0 != sK19
    | ~ element(X1,the_carrier(X0))
    | ~ latt_str(X0)
    | element(cast_to_el_of_LattPOSet(X0,X1),the_carrier(poset_of_lattice(X0)))
    | empty_carrier(X0) ),
    inference(resolution_lifted,[status(thm)],[c_81,c_152]) ).

cnf(c_2605,plain,
    ( ~ element(X0,the_carrier(sK19))
    | ~ latt_str(sK19)
    | element(cast_to_el_of_LattPOSet(sK19,X0),the_carrier(poset_of_lattice(sK19)))
    | empty_carrier(sK19) ),
    inference(unflattening,[status(thm)],[c_2604]) ).

cnf(c_2628,plain,
    ( X0 != sK19
    | ~ 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_63,c_152]) ).

cnf(c_2629,plain,
    ( ~ element(X0,the_carrier(sK19))
    | ~ latt_str(sK19)
    | cast_to_el_of_LattPOSet(sK19,X0) = X0
    | empty_carrier(sK19) ),
    inference(unflattening,[status(thm)],[c_2628]) ).

cnf(c_2631,plain,
    ( cast_to_el_of_LattPOSet(sK19,X0) = X0
    | ~ element(X0,the_carrier(sK19)) ),
    inference(global_subsumption_just,[status(thm)],[c_2629,c_151,c_153,c_2629]) ).

cnf(c_2632,plain,
    ( ~ element(X0,the_carrier(sK19))
    | cast_to_el_of_LattPOSet(sK19,X0) = X0 ),
    inference(renaming,[status(thm)],[c_2631]) ).

cnf(c_2785,plain,
    ( X0 != sK19
    | ~ element(X1,the_carrier(X0))
    | element(sK0(X0,X1,X2),the_carrier(X0))
    | latt_set_smaller(X0,X1,X2)
    | empty_carrier(X0) ),
    inference(resolution_lifted,[status(thm)],[c_60,c_151]) ).

cnf(c_2786,plain,
    ( ~ element(X0,the_carrier(sK19))
    | element(sK0(sK19,X0,X1),the_carrier(sK19))
    | latt_set_smaller(sK19,X0,X1)
    | empty_carrier(sK19) ),
    inference(unflattening,[status(thm)],[c_2785]) ).

cnf(c_2788,plain,
    ( latt_set_smaller(sK19,X0,X1)
    | element(sK0(sK19,X0,X1),the_carrier(sK19))
    | ~ element(X0,the_carrier(sK19)) ),
    inference(global_subsumption_just,[status(thm)],[c_2786,c_153,c_2786]) ).

cnf(c_2789,plain,
    ( ~ element(X0,the_carrier(sK19))
    | element(sK0(sK19,X0,X1),the_carrier(sK19))
    | latt_set_smaller(sK19,X0,X1) ),
    inference(renaming,[status(thm)],[c_2788]) ).

cnf(c_2800,plain,
    ( X0 != sK19
    | ~ element(X1,the_carrier(X0))
    | in(sK0(X0,X1,X2),X2)
    | latt_set_smaller(X0,X1,X2)
    | empty_carrier(X0) ),
    inference(resolution_lifted,[status(thm)],[c_59,c_151]) ).

cnf(c_2801,plain,
    ( ~ element(X0,the_carrier(sK19))
    | in(sK0(sK19,X0,X1),X1)
    | latt_set_smaller(sK19,X0,X1)
    | empty_carrier(sK19) ),
    inference(unflattening,[status(thm)],[c_2800]) ).

cnf(c_2803,plain,
    ( latt_set_smaller(sK19,X0,X1)
    | in(sK0(sK19,X0,X1),X1)
    | ~ element(X0,the_carrier(sK19)) ),
    inference(global_subsumption_just,[status(thm)],[c_2801,c_153,c_2801]) ).

cnf(c_2804,plain,
    ( ~ element(X0,the_carrier(sK19))
    | in(sK0(sK19,X0,X1),X1)
    | latt_set_smaller(sK19,X0,X1) ),
    inference(renaming,[status(thm)],[c_2803]) ).

cnf(c_6088,plain,
    ( ~ element(X0,the_carrier(sK19))
    | element(cast_to_el_of_LattPOSet(sK19,X0),the_carrier(poset_of_lattice(sK19))) ),
    inference(prop_impl_just,[status(thm)],[c_151,c_153,c_2605]) ).

cnf(c_6090,plain,
    ( ~ element(X0,the_carrier(sK19))
    | cast_to_el_of_LattPOSet(sK19,X0) = X0 ),
    inference(prop_impl_just,[status(thm)],[c_2632]) ).

cnf(c_9644,plain,
    ( X0 != X1
    | X2 != X1
    | X2 = X0 ),
    theory(equality) ).

cnf(c_9649,plain,
    ( X0 != X1
    | ~ in(X1,X2)
    | in(X0,X2) ),
    theory(equality) ).

cnf(c_9653,plain,
    ( X0 != X1
    | X2 != X3
    | ~ element(X1,X3)
    | element(X0,X2) ),
    theory(equality) ).

cnf(c_9658,plain,
    ( X0 != X1
    | X2 != X3
    | X4 != X5
    | ~ relstr_element_smaller(X1,X3,X5)
    | relstr_element_smaller(X0,X2,X4) ),
    theory(equality) ).

cnf(c_9668,plain,
    ( X0 != X1
    | X2 != X3
    | X4 != X5
    | ~ related_reflexive(X1,X3,X5)
    | related_reflexive(X0,X2,X4) ),
    theory(equality) ).

cnf(c_11603,plain,
    ( ~ element(sK20,the_carrier(sK19))
    | element(sK0(sK19,sK20,X0),the_carrier(sK19))
    | latt_set_smaller(sK19,sK20,X0) ),
    inference(instantiation,[status(thm)],[c_2789]) ).

cnf(c_11627,plain,
    ( ~ related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,sK20),cast_to_el_of_LattPOSet(sK19,sK0(sK19,sK20,X0)))
    | ~ element(sK20,the_carrier(sK19))
    | latt_set_smaller(sK19,sK20,X0) ),
    inference(instantiation,[status(thm)],[c_2475]) ).

cnf(c_11638,plain,
    ( ~ element(sK20,the_carrier(sK19))
    | in(sK0(sK19,sK20,X0),X0)
    | latt_set_smaller(sK19,sK20,X0) ),
    inference(instantiation,[status(thm)],[c_2804]) ).

cnf(c_11709,plain,
    ( ~ element(sK20,the_carrier(sK19))
    | element(sK0(sK19,sK20,sK18),the_carrier(sK19))
    | latt_set_smaller(sK19,sK20,sK18) ),
    inference(instantiation,[status(thm)],[c_11603]) ).

cnf(c_11716,plain,
    ( ~ related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,sK20),cast_to_el_of_LattPOSet(sK19,sK0(sK19,sK20,sK18)))
    | ~ element(sK20,the_carrier(sK19))
    | latt_set_smaller(sK19,sK20,sK18) ),
    inference(instantiation,[status(thm)],[c_11627]) ).

cnf(c_11721,plain,
    ( ~ element(sK20,the_carrier(sK19))
    | in(sK0(sK19,sK20,sK18),sK18)
    | latt_set_smaller(sK19,sK20,sK18) ),
    inference(instantiation,[status(thm)],[c_11638]) ).

cnf(c_11854,plain,
    ( ~ related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,sK20),sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)))
    | ~ element(cast_to_el_of_LattPOSet(sK19,sK20),the_carrier(poset_of_lattice(sK19)))
    | ~ rel_str(poset_of_lattice(sK19))
    | ~ reflexive_relstr(poset_of_lattice(sK19))
    | relstr_element_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
    | empty_carrier(poset_of_lattice(sK19)) ),
    inference(instantiation,[status(thm)],[c_1528]) ).

cnf(c_12476,plain,
    ( ~ element(X0,the_carrier(poset_of_lattice(sK19)))
    | ~ rel_str(poset_of_lattice(sK19))
    | in(sK1(poset_of_lattice(sK19),X1,X0),X1)
    | relstr_element_smaller(poset_of_lattice(sK19),X1,X0) ),
    inference(instantiation,[status(thm)],[c_66]) ).

cnf(c_12583,plain,
    ( ~ element(sK20,the_carrier(sK19))
    | element(cast_to_el_of_LattPOSet(sK19,sK20),the_carrier(poset_of_lattice(sK19))) ),
    inference(instantiation,[status(thm)],[c_6088]) ).

cnf(c_15283,plain,
    ( rel_str_of(X0,X1) != poset_of_lattice(sK19)
    | ~ relation_of2(k2_lattice3(sK19),the_carrier(sK19),the_carrier(sK19))
    | the_carrier(sK19) = X0 ),
    inference(superposition,[status(thm)],[c_2572,c_118]) ).

cnf(c_15285,plain,
    ( rel_str_of(X0,X1) != poset_of_lattice(sK19)
    | ~ relation_of2(X1,X0,X0)
    | the_carrier(sK19) = X0 ),
    inference(superposition,[status(thm)],[c_2572,c_118]) ).

cnf(c_15794,plain,
    ( rel_str_of(X0,X1) != poset_of_lattice(sK19)
    | the_carrier(sK19) = X0 ),
    inference(global_subsumption_just,[status(thm)],[c_15285,c_152,c_151,c_153,c_1314,c_15283]) ).

cnf(c_17032,plain,
    ( ~ element(cast_to_el_of_LattPOSet(sK19,sK20),the_carrier(poset_of_lattice(sK19)))
    | ~ rel_str(poset_of_lattice(sK19))
    | in(sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),sK18)
    | relstr_element_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)) ),
    inference(instantiation,[status(thm)],[c_12476]) ).

cnf(c_19671,plain,
    ( ~ element(sK0(sK19,sK20,sK18),the_carrier(sK19))
    | element(cast_to_el_of_LattPOSet(sK19,sK0(sK19,sK20,sK18)),the_carrier(poset_of_lattice(sK19))) ),
    inference(instantiation,[status(thm)],[c_6088]) ).

cnf(c_19738,plain,
    ( ~ element(sK0(sK19,sK20,sK18),the_carrier(sK19))
    | cast_to_el_of_LattPOSet(sK19,sK0(sK19,sK20,sK18)) = sK0(sK19,sK20,sK18) ),
    inference(instantiation,[status(thm)],[c_6090]) ).

cnf(c_22756,plain,
    ( X0 != poset_of_lattice(sK19)
    | rel_str_of(the_carrier(sK19),k2_lattice3(sK19)) = X0 ),
    inference(resolution,[status(thm)],[c_9644,c_2572]) ).

cnf(c_30666,plain,
    ( rel_str_of(X0,X1) != poset_of_lattice(sK19)
    | ~ relation_of2(k2_lattice3(sK19),the_carrier(sK19),the_carrier(sK19))
    | the_carrier(sK19) = X0 ),
    inference(resolution,[status(thm)],[c_118,c_22756]) ).

cnf(c_33296,plain,
    ( ~ element(sK1(X0,X1,X2),the_carrier(sK19))
    | ~ in(sK1(X0,X1,X2),X1)
    | ~ latt_set_smaller(sK19,X3,X1)
    | ~ element(X3,the_carrier(sK19))
    | related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,X3),cast_to_el_of_LattPOSet(sK19,sK1(X0,X1,X2))) ),
    inference(instantiation,[status(thm)],[c_2455]) ).

cnf(c_33327,plain,
    ( ~ element(cast_to_el_of_LattPOSet(sK19,sK0(sK19,sK20,sK18)),the_carrier(poset_of_lattice(sK19)))
    | ~ in(cast_to_el_of_LattPOSet(sK19,sK0(sK19,sK20,sK18)),X0)
    | ~ relstr_element_smaller(poset_of_lattice(sK19),X0,cast_to_el_of_LattPOSet(sK19,sK20))
    | ~ element(cast_to_el_of_LattPOSet(sK19,sK20),the_carrier(poset_of_lattice(sK19)))
    | ~ rel_str(poset_of_lattice(sK19))
    | ~ reflexive_relstr(poset_of_lattice(sK19))
    | related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,sK20),cast_to_el_of_LattPOSet(sK19,sK0(sK19,sK20,sK18)))
    | empty_carrier(poset_of_lattice(sK19)) ),
    inference(instantiation,[status(thm)],[c_1537]) ).

cnf(c_33392,plain,
    ( X0 != sK0(sK19,sK20,sK18)
    | ~ in(sK0(sK19,sK20,sK18),sK18)
    | in(X0,sK18) ),
    inference(instantiation,[status(thm)],[c_9649]) ).

cnf(c_33648,plain,
    ( cast_to_el_of_LattPOSet(sK19,sK0(sK19,sK20,sK18)) != sK0(sK19,sK20,sK18)
    | ~ in(sK0(sK19,sK20,sK18),sK18)
    | in(cast_to_el_of_LattPOSet(sK19,sK0(sK19,sK20,sK18)),sK18) ),
    inference(instantiation,[status(thm)],[c_33392]) ).

cnf(c_33894,plain,
    ( ~ element(cast_to_el_of_LattPOSet(sK19,sK0(sK19,sK20,sK18)),the_carrier(poset_of_lattice(sK19)))
    | ~ in(cast_to_el_of_LattPOSet(sK19,sK0(sK19,sK20,sK18)),sK18)
    | ~ element(cast_to_el_of_LattPOSet(sK19,sK20),the_carrier(poset_of_lattice(sK19)))
    | ~ relstr_element_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
    | ~ rel_str(poset_of_lattice(sK19))
    | ~ reflexive_relstr(poset_of_lattice(sK19))
    | related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,sK20),cast_to_el_of_LattPOSet(sK19,sK0(sK19,sK20,sK18)))
    | empty_carrier(poset_of_lattice(sK19)) ),
    inference(instantiation,[status(thm)],[c_33327]) ).

cnf(c_34724,plain,
    ( ~ element(X0,the_carrier(poset_of_lattice(sK19)))
    | ~ rel_str(poset_of_lattice(sK19))
    | element(sK1(poset_of_lattice(sK19),X1,X0),the_carrier(poset_of_lattice(sK19)))
    | relstr_element_smaller(poset_of_lattice(sK19),X1,X0) ),
    inference(instantiation,[status(thm)],[c_67]) ).

cnf(c_36536,plain,
    ( ~ element(sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),the_carrier(sK19))
    | ~ in(sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),sK18)
    | ~ latt_set_smaller(sK19,X0,sK18)
    | ~ element(X0,the_carrier(sK19))
    | related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,X0),cast_to_el_of_LattPOSet(sK19,sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)))) ),
    inference(instantiation,[status(thm)],[c_33296]) ).

cnf(c_41496,plain,
    ( ~ element(cast_to_el_of_LattPOSet(sK19,sK20),the_carrier(poset_of_lattice(sK19)))
    | ~ rel_str(poset_of_lattice(sK19))
    | element(sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),the_carrier(poset_of_lattice(sK19)))
    | relstr_element_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)) ),
    inference(instantiation,[status(thm)],[c_34724]) ).

cnf(c_49890,plain,
    ( X0 != poset_of_lattice(sK19)
    | X1 != sK18
    | X2 != cast_to_el_of_LattPOSet(sK19,sK20)
    | relstr_element_smaller(X0,X1,X2)
    | latt_set_smaller(sK19,sK20,sK18) ),
    inference(resolution,[status(thm)],[c_9658,c_149]) ).

cnf(c_50147,plain,
    latt_set_smaller(sK19,sK20,sK18),
    inference(global_subsumption_just,[status(thm)],[c_49890,c_152,c_151,c_153,c_150,c_149,c_200,c_204,c_208,c_11709,c_11716,c_11721,c_12583,c_19671,c_19738,c_33648,c_33894]) ).

cnf(c_62462,plain,
    ( ~ element(sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),the_carrier(sK19))
    | ~ in(sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),sK18)
    | ~ latt_set_smaller(sK19,sK20,sK18)
    | ~ element(sK20,the_carrier(sK19))
    | related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,sK20),cast_to_el_of_LattPOSet(sK19,sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)))) ),
    inference(instantiation,[status(thm)],[c_36536]) ).

cnf(c_84497,plain,
    ( rel_str_of(X0,X1) != poset_of_lattice(sK19)
    | the_carrier(sK19) = X0 ),
    inference(global_subsumption_just,[status(thm)],[c_30666,c_15794]) ).

cnf(c_84509,plain,
    ( ~ strict_rel_str(poset_of_lattice(sK19))
    | ~ rel_str(poset_of_lattice(sK19))
    | the_carrier(sK19) = the_carrier(poset_of_lattice(sK19)) ),
    inference(resolution,[status(thm)],[c_84497,c_49]) ).

cnf(c_107023,plain,
    ( sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)) != X0
    | cast_to_el_of_LattPOSet(sK19,sK20) != X1
    | poset_of_lattice(sK19) != X2
    | ~ related_reflexive(X2,X1,X0)
    | related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,sK20),sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))) ),
    inference(instantiation,[status(thm)],[c_9668]) ).

cnf(c_107315,plain,
    ( sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)) != X0
    | cast_to_el_of_LattPOSet(sK19,sK20) != X1
    | poset_of_lattice(sK19) != poset_of_lattice(sK19)
    | ~ related_reflexive(poset_of_lattice(sK19),X1,X0)
    | related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,sK20),sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))) ),
    inference(instantiation,[status(thm)],[c_107023]) ).

cnf(c_107316,plain,
    ( sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)) != X0
    | cast_to_el_of_LattPOSet(sK19,sK20) != X1
    | ~ related_reflexive(poset_of_lattice(sK19),X1,X0)
    | related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,sK20),sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))) ),
    inference(equality_resolution_simp,[status(thm)],[c_107315]) ).

cnf(c_107339,plain,
    ( X0 != sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
    | X1 != the_carrier(poset_of_lattice(sK19))
    | ~ element(sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),the_carrier(poset_of_lattice(sK19)))
    | element(X0,X1) ),
    inference(instantiation,[status(thm)],[c_9653]) ).

cnf(c_107412,plain,
    ( ~ element(sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),the_carrier(sK19))
    | cast_to_el_of_LattPOSet(sK19,sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))) = sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)) ),
    inference(instantiation,[status(thm)],[c_6090]) ).

cnf(c_107915,plain,
    ( sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)) != X0
    | X1 != X0
    | sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)) = X1 ),
    inference(instantiation,[status(thm)],[c_9644]) ).

cnf(c_107977,plain,
    ( sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)) != X0
    | cast_to_el_of_LattPOSet(sK19,sK20) != cast_to_el_of_LattPOSet(sK19,sK20)
    | ~ related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,sK20),X0)
    | related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,sK20),sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))) ),
    inference(instantiation,[status(thm)],[c_107316]) ).

cnf(c_107978,plain,
    ( sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)) != X0
    | ~ related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,sK20),X0)
    | related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,sK20),sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))) ),
    inference(equality_resolution_simp,[status(thm)],[c_107977]) ).

cnf(c_108019,plain,
    ( the_carrier(X0) != the_carrier(poset_of_lattice(sK19))
    | X1 != sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
    | ~ element(sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),the_carrier(poset_of_lattice(sK19)))
    | element(X1,the_carrier(X0)) ),
    inference(instantiation,[status(thm)],[c_107339]) ).

cnf(c_109297,plain,
    ( sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)) != cast_to_el_of_LattPOSet(sK19,X0)
    | ~ related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,sK20),cast_to_el_of_LattPOSet(sK19,X0))
    | related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,sK20),sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))) ),
    inference(instantiation,[status(thm)],[c_107978]) ).

cnf(c_111285,plain,
    ( sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)) != sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
    | X0 != sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
    | sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)) = X0 ),
    inference(instantiation,[status(thm)],[c_107915]) ).

cnf(c_111286,plain,
    ( X0 != sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
    | sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)) = X0 ),
    inference(equality_resolution_simp,[status(thm)],[c_111285]) ).

cnf(c_111879,plain,
    ( sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)) != sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
    | the_carrier(X0) != the_carrier(poset_of_lattice(sK19))
    | ~ element(sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),the_carrier(poset_of_lattice(sK19)))
    | element(sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),the_carrier(X0)) ),
    inference(instantiation,[status(thm)],[c_108019]) ).

cnf(c_111880,plain,
    ( the_carrier(X0) != the_carrier(poset_of_lattice(sK19))
    | ~ element(sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),the_carrier(poset_of_lattice(sK19)))
    | element(sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),the_carrier(X0)) ),
    inference(equality_resolution_simp,[status(thm)],[c_111879]) ).

cnf(c_111881,plain,
    ( the_carrier(sK19) != the_carrier(poset_of_lattice(sK19))
    | ~ element(sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),the_carrier(poset_of_lattice(sK19)))
    | element(sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),the_carrier(sK19)) ),
    inference(instantiation,[status(thm)],[c_111880]) ).

cnf(c_122014,plain,
    ( cast_to_el_of_LattPOSet(sK19,sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))) != sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
    | sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)) = cast_to_el_of_LattPOSet(sK19,sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))) ),
    inference(instantiation,[status(thm)],[c_111286]) ).

cnf(c_245901,plain,
    ( sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)) != cast_to_el_of_LattPOSet(sK19,sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)))
    | ~ related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,sK20),cast_to_el_of_LattPOSet(sK19,sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))))
    | related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,sK20),sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))) ),
    inference(instantiation,[status(thm)],[c_109297]) ).

cnf(c_245902,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_245901,c_122014,c_111881,c_107412,c_84509,c_62462,c_50147,c_41496,c_17032,c_12583,c_11854,c_148,c_208,c_204,c_200,c_199,c_150,c_153,c_151,c_152]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem  : SEU347+1 : TPTP v8.1.2. Released v3.3.0.
% 0.05/0.11  % Command  : run_iprover %s %d THM
% 0.10/0.31  % Computer : n010.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Thu May  2 17:37:04 EDT 2024
% 0.10/0.31  % CPUTime  : 
% 0.16/0.42  Running first-order theorem proving
% 0.16/0.42  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 170.15/23.23  % SZS status Started for theBenchmark.p
% 170.15/23.23  % SZS status Theorem for theBenchmark.p
% 170.15/23.23  
% 170.15/23.23  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 170.15/23.23  
% 170.15/23.23  ------  iProver source info
% 170.15/23.23  
% 170.15/23.23  git: date: 2024-05-02 19:28:25 +0000
% 170.15/23.23  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 170.15/23.23  git: non_committed_changes: false
% 170.15/23.23  
% 170.15/23.23  ------ Parsing...
% 170.15/23.23  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 170.15/23.23  
% 170.15/23.23  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe_e  sup_sim: 0  sf_s  rm: 13 0s  sf_e  pe_s  pe_e 
% 170.15/23.23  
% 170.15/23.23  ------ Preprocessing... gs_s  sp: 4 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 170.15/23.23  
% 170.15/23.23  ------ Preprocessing... sf_s  rm: 4 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 170.15/23.23  ------ Proving...
% 170.15/23.23  ------ Problem Properties 
% 170.15/23.23  
% 170.15/23.23  
% 170.15/23.23  clauses                                 105
% 170.15/23.23  conjectures                             4
% 170.15/23.23  EPR                                     22
% 170.15/23.23  Horn                                    84
% 170.15/23.23  unary                                   42
% 170.15/23.23  binary                                  32
% 170.15/23.23  lits                                    228
% 170.15/23.23  lits eq                                 12
% 170.15/23.23  fd_pure                                 0
% 170.15/23.23  fd_pseudo                               0
% 170.15/23.23  fd_cond                                 1
% 170.15/23.23  fd_pseudo_cond                          3
% 170.15/23.23  AC symbols                              0
% 170.15/23.23  
% 170.15/23.23  ------ Input Options Time Limit: Unbounded
% 170.15/23.23  
% 170.15/23.23  
% 170.15/23.23  ------ 
% 170.15/23.23  Current options:
% 170.15/23.23  ------ 
% 170.15/23.23  
% 170.15/23.23  
% 170.15/23.23  
% 170.15/23.23  
% 170.15/23.23  ------ Proving...
% 170.15/23.23  
% 170.15/23.23  
% 170.15/23.23  % SZS status Theorem for theBenchmark.p
% 170.15/23.23  
% 170.15/23.23  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 170.15/23.23  
% 170.15/23.23  
%------------------------------------------------------------------------------