TSTP Solution File: SEU346+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SEU346+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n023.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  : 600s
% DateTime : Tue Jul 19 09:19:12 EDT 2022

% Result   : Theorem 0.27s 6.45s
% Output   : CNFRefutation 0.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   25
% Syntax   : Number of formulae    :  140 (  28 unt;   0 def)
%            Number of atoms       :  576 (  50 equ)
%            Maximal formula atoms :   20 (   4 avg)
%            Number of connectives :  732 ( 296   ~; 328   |;  70   &)
%                                         (   6 <=>;  32  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   23 (  21 usr;   1 prp; 0-3 aty)
%            Number of functors    :   15 (  15 usr;   3 con; 0-4 aty)
%            Number of variables   :  230 (  13 sgn 103   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(redefinition_m2_relset_1,axiom,
    ! [X1,X2,X3] :
      ( relation_of2_as_subset(X3,X1,X2)
    <=> relation_of2(X3,X1,X2) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',redefinition_m2_relset_1) ).

fof(dt_k2_lattice3,axiom,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & lattice(X1)
        & latt_str(X1) )
     => ( reflexive(k2_lattice3(X1))
        & antisymmetric(k2_lattice3(X1))
        & transitive(k2_lattice3(X1))
        & v1_partfun1(k2_lattice3(X1),the_carrier(X1),the_carrier(X1))
        & relation_of2_as_subset(k2_lattice3(X1),the_carrier(X1),the_carrier(X1)) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',dt_k2_lattice3) ).

fof(free_g1_orders_2,axiom,
    ! [X1,X2] :
      ( relation_of2(X2,X1,X1)
     => ! [X3,X4] :
          ( rel_str_of(X1,X2) = rel_str_of(X3,X4)
         => ( X1 = X3
            & X2 = X4 ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',free_g1_orders_2) ).

fof(d2_lattice3,axiom,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & lattice(X1)
        & latt_str(X1) )
     => poset_of_lattice(X1) = rel_str_of(the_carrier(X1),k2_lattice3(X1)) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d2_lattice3) ).

fof(abstractness_v1_orders_2,axiom,
    ! [X1] :
      ( rel_str(X1)
     => ( strict_rel_str(X1)
       => X1 = rel_str_of(the_carrier(X1),the_InternalRel(X1)) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',abstractness_v1_orders_2) ).

fof(t7_lattice3,conjecture,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & lattice(X1)
        & latt_str(X1) )
     => ! [X2] :
          ( element(X2,the_carrier(X1))
         => ! [X3] :
              ( element(X3,the_carrier(X1))
             => ( below_refl(X1,X2,X3)
              <=> related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3)) ) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t7_lattice3) ).

fof(fc4_lattice3,axiom,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & lattice(X1)
        & latt_str(X1) )
     => ( ~ empty_carrier(poset_of_lattice(X1))
        & strict_rel_str(poset_of_lattice(X1))
        & reflexive_relstr(poset_of_lattice(X1))
        & transitive_relstr(poset_of_lattice(X1))
        & antisymmetric_relstr(poset_of_lattice(X1)) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fc4_lattice3) ).

fof(fc1_struct_0,axiom,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & one_sorted_str(X1) )
     => ~ empty(the_carrier(X1)) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fc1_struct_0) ).

fof(dt_k3_lattice3,axiom,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & lattice(X1)
        & latt_str(X1) )
     => ( strict_rel_str(poset_of_lattice(X1))
        & reflexive_relstr(poset_of_lattice(X1))
        & transitive_relstr(poset_of_lattice(X1))
        & antisymmetric_relstr(poset_of_lattice(X1))
        & rel_str(poset_of_lattice(X1)) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',dt_k3_lattice3) ).

fof(d9_orders_2,axiom,
    ! [X1] :
      ( rel_str(X1)
     => ! [X2] :
          ( element(X2,the_carrier(X1))
         => ! [X3] :
              ( element(X3,the_carrier(X1))
             => ( related(X1,X2,X3)
              <=> in(ordered_pair(X2,X3),the_InternalRel(X1)) ) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d9_orders_2) ).

fof(d5_tarski,axiom,
    ! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d5_tarski) ).

fof(d3_lattice3,axiom,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & lattice(X1)
        & latt_str(X1) )
     => ! [X2] :
          ( element(X2,the_carrier(X1))
         => cast_to_el_of_LattPOSet(X1,X2) = X2 ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d3_lattice3) ).

fof(commutativity_k2_tarski,axiom,
    ! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',commutativity_k2_tarski) ).

fof(dt_u1_orders_2,axiom,
    ! [X1] :
      ( rel_str(X1)
     => relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1)) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',dt_u1_orders_2) ).

fof(redefinition_r3_orders_2,axiom,
    ! [X1,X2,X3] :
      ( ( ~ empty_carrier(X1)
        & reflexive_relstr(X1)
        & rel_str(X1)
        & element(X2,the_carrier(X1))
        & element(X3,the_carrier(X1)) )
     => ( related_reflexive(X1,X2,X3)
      <=> related(X1,X2,X3) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',redefinition_r3_orders_2) ).

fof(dt_l1_orders_2,axiom,
    ! [X1] :
      ( rel_str(X1)
     => one_sorted_str(X1) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',dt_l1_orders_2) ).

fof(redefinition_k1_domain_1,axiom,
    ! [X1,X2,X3,X4] :
      ( ( ~ empty(X1)
        & ~ empty(X2)
        & element(X3,X1)
        & element(X4,X2) )
     => ordered_pair_as_product_element(X1,X2,X3,X4) = ordered_pair(X3,X4) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',redefinition_k1_domain_1) ).

fof(fc1_orders_2,axiom,
    ! [X1,X2] :
      ( ( ~ empty(X1)
        & relation_of2(X2,X1,X1) )
     => ( ~ empty_carrier(rel_str_of(X1,X2))
        & strict_rel_str(rel_str_of(X1,X2)) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fc1_orders_2) ).

fof(t32_filter_1,axiom,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & lattice(X1)
        & latt_str(X1) )
     => ! [X2] :
          ( element(X2,the_carrier(X1))
         => ! [X3] :
              ( element(X3,the_carrier(X1))
             => ( in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1))
              <=> below_refl(X1,X2,X3) ) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t32_filter_1) ).

fof(redefinition_k2_lattice3,axiom,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & lattice(X1)
        & latt_str(X1) )
     => k2_lattice3(X1) = relation_of_lattice(X1) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',redefinition_k2_lattice3) ).

fof(reflexivity_r3_orders_2,axiom,
    ! [X1,X2,X3] :
      ( ( ~ empty_carrier(X1)
        & reflexive_relstr(X1)
        & rel_str(X1)
        & element(X2,the_carrier(X1))
        & element(X3,the_carrier(X1)) )
     => related_reflexive(X1,X2,X2) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',reflexivity_r3_orders_2) ).

fof(existence_m1_subset_1,axiom,
    ! [X1] :
    ? [X2] : element(X2,X1),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',existence_m1_subset_1) ).

fof(t1_subset,axiom,
    ! [X1,X2] :
      ( in(X1,X2)
     => element(X1,X2) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t1_subset) ).

fof(t7_boole,axiom,
    ! [X1,X2] :
      ~ ( in(X1,X2)
        & empty(X2) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t7_boole) ).

fof(t2_subset,axiom,
    ! [X1,X2] :
      ( element(X1,X2)
     => ( empty(X2)
        | in(X1,X2) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t2_subset) ).

fof(c_0_25,plain,
    ! [X4,X5,X6,X4,X5,X6] :
      ( ( ~ relation_of2_as_subset(X6,X4,X5)
        | relation_of2(X6,X4,X5) )
      & ( ~ relation_of2(X6,X4,X5)
        | relation_of2_as_subset(X6,X4,X5) ) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])])])]) ).

fof(c_0_26,plain,
    ! [X2] :
      ( ( reflexive(k2_lattice3(X2))
        | empty_carrier(X2)
        | ~ lattice(X2)
        | ~ latt_str(X2) )
      & ( antisymmetric(k2_lattice3(X2))
        | empty_carrier(X2)
        | ~ lattice(X2)
        | ~ latt_str(X2) )
      & ( transitive(k2_lattice3(X2))
        | empty_carrier(X2)
        | ~ lattice(X2)
        | ~ latt_str(X2) )
      & ( v1_partfun1(k2_lattice3(X2),the_carrier(X2),the_carrier(X2))
        | empty_carrier(X2)
        | ~ lattice(X2)
        | ~ latt_str(X2) )
      & ( relation_of2_as_subset(k2_lattice3(X2),the_carrier(X2),the_carrier(X2))
        | empty_carrier(X2)
        | ~ lattice(X2)
        | ~ latt_str(X2) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k2_lattice3])])])]) ).

fof(c_0_27,plain,
    ! [X5,X6,X7,X8] :
      ( ( X5 = X7
        | rel_str_of(X5,X6) != rel_str_of(X7,X8)
        | ~ relation_of2(X6,X5,X5) )
      & ( X6 = X8
        | rel_str_of(X5,X6) != rel_str_of(X7,X8)
        | ~ relation_of2(X6,X5,X5) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[free_g1_orders_2])])])])])]) ).

cnf(c_0_28,plain,
    ( relation_of2(X1,X2,X3)
    | ~ relation_of2_as_subset(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_29,plain,
    ( empty_carrier(X1)
    | relation_of2_as_subset(k2_lattice3(X1),the_carrier(X1),the_carrier(X1))
    | ~ latt_str(X1)
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_30,plain,
    ( X2 = X3
    | ~ relation_of2(X1,X2,X2)
    | rel_str_of(X2,X1) != rel_str_of(X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_31,plain,
    ( relation_of2(k2_lattice3(X1),the_carrier(X1),the_carrier(X1))
    | empty_carrier(X1)
    | ~ lattice(X1)
    | ~ latt_str(X1) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

fof(c_0_32,plain,
    ! [X2] :
      ( empty_carrier(X2)
      | ~ lattice(X2)
      | ~ latt_str(X2)
      | poset_of_lattice(X2) = rel_str_of(the_carrier(X2),k2_lattice3(X2)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d2_lattice3])])]) ).

cnf(c_0_33,plain,
    ( the_carrier(X1) = X2
    | empty_carrier(X1)
    | rel_str_of(the_carrier(X1),k2_lattice3(X1)) != rel_str_of(X2,X3)
    | ~ lattice(X1)
    | ~ latt_str(X1) ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_34,plain,
    ( poset_of_lattice(X1) = rel_str_of(the_carrier(X1),k2_lattice3(X1))
    | empty_carrier(X1)
    | ~ latt_str(X1)
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

fof(c_0_35,plain,
    ! [X2] :
      ( ~ rel_str(X2)
      | ~ strict_rel_str(X2)
      | X2 = rel_str_of(the_carrier(X2),the_InternalRel(X2)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[abstractness_v1_orders_2])]) ).

fof(c_0_36,negated_conjecture,
    ~ ! [X1] :
        ( ( ~ empty_carrier(X1)
          & lattice(X1)
          & latt_str(X1) )
       => ! [X2] :
            ( element(X2,the_carrier(X1))
           => ! [X3] :
                ( element(X3,the_carrier(X1))
               => ( below_refl(X1,X2,X3)
                <=> related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3)) ) ) ) ),
    inference(assume_negation,[status(cth)],[t7_lattice3]) ).

fof(c_0_37,plain,
    ! [X2] :
      ( ( ~ empty_carrier(poset_of_lattice(X2))
        | empty_carrier(X2)
        | ~ lattice(X2)
        | ~ latt_str(X2) )
      & ( strict_rel_str(poset_of_lattice(X2))
        | empty_carrier(X2)
        | ~ lattice(X2)
        | ~ latt_str(X2) )
      & ( reflexive_relstr(poset_of_lattice(X2))
        | empty_carrier(X2)
        | ~ lattice(X2)
        | ~ latt_str(X2) )
      & ( transitive_relstr(poset_of_lattice(X2))
        | empty_carrier(X2)
        | ~ lattice(X2)
        | ~ latt_str(X2) )
      & ( antisymmetric_relstr(poset_of_lattice(X2))
        | empty_carrier(X2)
        | ~ lattice(X2)
        | ~ latt_str(X2) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc4_lattice3])])])]) ).

fof(c_0_38,plain,
    ! [X2] :
      ( empty_carrier(X2)
      | ~ one_sorted_str(X2)
      | ~ empty(the_carrier(X2)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc1_struct_0])])]) ).

cnf(c_0_39,plain,
    ( the_carrier(X1) = X2
    | empty_carrier(X1)
    | poset_of_lattice(X1) != rel_str_of(X2,X3)
    | ~ lattice(X1)
    | ~ latt_str(X1) ),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_40,plain,
    ( X1 = rel_str_of(the_carrier(X1),the_InternalRel(X1))
    | ~ strict_rel_str(X1)
    | ~ rel_str(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

fof(c_0_41,plain,
    ! [X2] :
      ( ( strict_rel_str(poset_of_lattice(X2))
        | empty_carrier(X2)
        | ~ lattice(X2)
        | ~ latt_str(X2) )
      & ( reflexive_relstr(poset_of_lattice(X2))
        | empty_carrier(X2)
        | ~ lattice(X2)
        | ~ latt_str(X2) )
      & ( transitive_relstr(poset_of_lattice(X2))
        | empty_carrier(X2)
        | ~ lattice(X2)
        | ~ latt_str(X2) )
      & ( antisymmetric_relstr(poset_of_lattice(X2))
        | empty_carrier(X2)
        | ~ lattice(X2)
        | ~ latt_str(X2) )
      & ( rel_str(poset_of_lattice(X2))
        | empty_carrier(X2)
        | ~ lattice(X2)
        | ~ latt_str(X2) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k3_lattice3])])])]) ).

fof(c_0_42,plain,
    ! [X4,X5,X6] :
      ( ( ~ related(X4,X5,X6)
        | in(ordered_pair(X5,X6),the_InternalRel(X4))
        | ~ element(X6,the_carrier(X4))
        | ~ element(X5,the_carrier(X4))
        | ~ rel_str(X4) )
      & ( ~ in(ordered_pair(X5,X6),the_InternalRel(X4))
        | related(X4,X5,X6)
        | ~ element(X6,the_carrier(X4))
        | ~ element(X5,the_carrier(X4))
        | ~ rel_str(X4) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_orders_2])])])])])]) ).

fof(c_0_43,plain,
    ! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
    inference(variable_rename,[status(thm)],[d5_tarski]) ).

fof(c_0_44,negated_conjecture,
    ( ~ empty_carrier(esk20_0)
    & lattice(esk20_0)
    & latt_str(esk20_0)
    & element(esk21_0,the_carrier(esk20_0))
    & element(esk22_0,the_carrier(esk20_0))
    & ( ~ below_refl(esk20_0,esk21_0,esk22_0)
      | ~ related_reflexive(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk21_0),cast_to_el_of_LattPOSet(esk20_0,esk22_0)) )
    & ( below_refl(esk20_0,esk21_0,esk22_0)
      | related_reflexive(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk21_0),cast_to_el_of_LattPOSet(esk20_0,esk22_0)) ) ),
    inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_36])])])])])]) ).

cnf(c_0_45,plain,
    ( empty_carrier(X1)
    | ~ latt_str(X1)
    | ~ lattice(X1)
    | ~ empty_carrier(poset_of_lattice(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_46,plain,
    ( empty_carrier(X1)
    | ~ empty(the_carrier(X1))
    | ~ one_sorted_str(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_47,plain,
    ( the_carrier(X1) = the_carrier(X2)
    | empty_carrier(X1)
    | poset_of_lattice(X1) != X2
    | ~ lattice(X1)
    | ~ latt_str(X1)
    | ~ strict_rel_str(X2)
    | ~ rel_str(X2) ),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_48,plain,
    ( empty_carrier(X1)
    | rel_str(poset_of_lattice(X1))
    | ~ latt_str(X1)
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_49,plain,
    ( empty_carrier(X1)
    | strict_rel_str(poset_of_lattice(X1))
    | ~ latt_str(X1)
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

fof(c_0_50,plain,
    ! [X3,X4] :
      ( empty_carrier(X3)
      | ~ lattice(X3)
      | ~ latt_str(X3)
      | ~ element(X4,the_carrier(X3))
      | cast_to_el_of_LattPOSet(X3,X4) = X4 ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d3_lattice3])])])])])]) ).

cnf(c_0_51,plain,
    ( related(X1,X2,X3)
    | ~ rel_str(X1)
    | ~ element(X2,the_carrier(X1))
    | ~ element(X3,the_carrier(X1))
    | ~ in(ordered_pair(X2,X3),the_InternalRel(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_42]) ).

cnf(c_0_52,plain,
    ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

fof(c_0_53,plain,
    ! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
    inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).

fof(c_0_54,plain,
    ! [X2] :
      ( ~ rel_str(X2)
      | relation_of2_as_subset(the_InternalRel(X2),the_carrier(X2),the_carrier(X2)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_orders_2])]) ).

cnf(c_0_55,negated_conjecture,
    ~ empty_carrier(esk20_0),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_56,plain,
    ( empty_carrier(X1)
    | ~ one_sorted_str(poset_of_lattice(X1))
    | ~ empty(the_carrier(poset_of_lattice(X1)))
    | ~ lattice(X1)
    | ~ latt_str(X1) ),
    inference(spm,[status(thm)],[c_0_45,c_0_46]) ).

cnf(c_0_57,negated_conjecture,
    lattice(esk20_0),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_58,negated_conjecture,
    latt_str(esk20_0),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_59,plain,
    ( the_carrier(poset_of_lattice(X1)) = the_carrier(X1)
    | empty_carrier(X1)
    | ~ lattice(X1)
    | ~ latt_str(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_47]),c_0_48]),c_0_49]) ).

cnf(c_0_60,negated_conjecture,
    ( ~ related_reflexive(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk21_0),cast_to_el_of_LattPOSet(esk20_0,esk22_0))
    | ~ below_refl(esk20_0,esk21_0,esk22_0) ),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_61,plain,
    ( cast_to_el_of_LattPOSet(X1,X2) = X2
    | empty_carrier(X1)
    | ~ element(X2,the_carrier(X1))
    | ~ latt_str(X1)
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

cnf(c_0_62,negated_conjecture,
    element(esk22_0,the_carrier(esk20_0)),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

fof(c_0_63,plain,
    ! [X4,X5,X6] :
      ( ( ~ related_reflexive(X4,X5,X6)
        | related(X4,X5,X6)
        | empty_carrier(X4)
        | ~ reflexive_relstr(X4)
        | ~ rel_str(X4)
        | ~ element(X5,the_carrier(X4))
        | ~ element(X6,the_carrier(X4)) )
      & ( ~ related(X4,X5,X6)
        | related_reflexive(X4,X5,X6)
        | empty_carrier(X4)
        | ~ reflexive_relstr(X4)
        | ~ rel_str(X4)
        | ~ element(X5,the_carrier(X4))
        | ~ element(X6,the_carrier(X4)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_r3_orders_2])])])]) ).

cnf(c_0_64,plain,
    ( related(X1,X2,X3)
    | ~ rel_str(X1)
    | ~ element(X3,the_carrier(X1))
    | ~ element(X2,the_carrier(X1))
    | ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),the_InternalRel(X1)) ),
    inference(rw,[status(thm)],[c_0_51,c_0_52]) ).

cnf(c_0_65,plain,
    unordered_pair(X1,X2) = unordered_pair(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_53]) ).

cnf(c_0_66,plain,
    ( relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1))
    | ~ rel_str(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_54]) ).

cnf(c_0_67,negated_conjecture,
    ( ~ one_sorted_str(poset_of_lattice(esk20_0))
    | ~ empty(the_carrier(poset_of_lattice(esk20_0))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]),c_0_58])]) ).

cnf(c_0_68,negated_conjecture,
    the_carrier(poset_of_lattice(esk20_0)) = the_carrier(esk20_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_59]),c_0_57]),c_0_58])]) ).

fof(c_0_69,plain,
    ! [X2] :
      ( ~ rel_str(X2)
      | one_sorted_str(X2) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_orders_2])]) ).

fof(c_0_70,plain,
    ! [X5,X6,X7,X8] :
      ( empty(X5)
      | empty(X6)
      | ~ element(X7,X5)
      | ~ element(X8,X6)
      | ordered_pair_as_product_element(X5,X6,X7,X8) = ordered_pair(X7,X8) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_k1_domain_1])])]) ).

cnf(c_0_71,plain,
    ( in(ordered_pair(X2,X3),the_InternalRel(X1))
    | ~ rel_str(X1)
    | ~ element(X2,the_carrier(X1))
    | ~ element(X3,the_carrier(X1))
    | ~ related(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_42]) ).

cnf(c_0_72,negated_conjecture,
    ( ~ related_reflexive(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk21_0),esk22_0)
    | ~ below_refl(esk20_0,esk21_0,esk22_0) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]),c_0_57]),c_0_58])]),c_0_55]) ).

cnf(c_0_73,negated_conjecture,
    element(esk21_0,the_carrier(esk20_0)),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_74,plain,
    ( empty_carrier(X2)
    | related_reflexive(X2,X3,X1)
    | ~ element(X1,the_carrier(X2))
    | ~ element(X3,the_carrier(X2))
    | ~ rel_str(X2)
    | ~ reflexive_relstr(X2)
    | ~ related(X2,X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_63]) ).

cnf(c_0_75,plain,
    ( related(X1,X2,X3)
    | ~ element(X3,the_carrier(X1))
    | ~ element(X2,the_carrier(X1))
    | ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),the_InternalRel(X1))
    | ~ rel_str(X1) ),
    inference(rw,[status(thm)],[c_0_64,c_0_65]) ).

cnf(c_0_76,plain,
    ( empty_carrier(X1)
    | reflexive_relstr(poset_of_lattice(X1))
    | ~ latt_str(X1)
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

fof(c_0_77,plain,
    ! [X3,X4] :
      ( ( ~ empty_carrier(rel_str_of(X3,X4))
        | empty(X3)
        | ~ relation_of2(X4,X3,X3) )
      & ( strict_rel_str(rel_str_of(X3,X4))
        | empty(X3)
        | ~ relation_of2(X4,X3,X3) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc1_orders_2])])])]) ).

cnf(c_0_78,plain,
    ( relation_of2(the_InternalRel(X1),the_carrier(X1),the_carrier(X1))
    | ~ rel_str(X1) ),
    inference(spm,[status(thm)],[c_0_28,c_0_66]) ).

cnf(c_0_79,negated_conjecture,
    rel_str(poset_of_lattice(esk20_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_48]),c_0_57]),c_0_58])]) ).

cnf(c_0_80,negated_conjecture,
    strict_rel_str(poset_of_lattice(esk20_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_49]),c_0_57]),c_0_58])]) ).

cnf(c_0_81,negated_conjecture,
    ( ~ one_sorted_str(poset_of_lattice(esk20_0))
    | ~ empty(the_carrier(esk20_0)) ),
    inference(rw,[status(thm)],[c_0_67,c_0_68]) ).

cnf(c_0_82,plain,
    ( one_sorted_str(X1)
    | ~ rel_str(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_69]) ).

cnf(c_0_83,plain,
    ( ordered_pair_as_product_element(X1,X2,X3,X4) = ordered_pair(X3,X4)
    | empty(X2)
    | empty(X1)
    | ~ element(X4,X2)
    | ~ element(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_70]) ).

cnf(c_0_84,plain,
    ( X1 = X4
    | ~ relation_of2(X1,X2,X2)
    | rel_str_of(X2,X1) != rel_str_of(X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_85,plain,
    ( in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),the_InternalRel(X1))
    | ~ rel_str(X1)
    | ~ related(X1,X2,X3)
    | ~ element(X3,the_carrier(X1))
    | ~ element(X2,the_carrier(X1)) ),
    inference(rw,[status(thm)],[c_0_71,c_0_52]) ).

cnf(c_0_86,negated_conjecture,
    ( related_reflexive(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk21_0),cast_to_el_of_LattPOSet(esk20_0,esk22_0))
    | below_refl(esk20_0,esk21_0,esk22_0) ),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_87,negated_conjecture,
    ( ~ related_reflexive(poset_of_lattice(esk20_0),esk21_0,esk22_0)
    | ~ below_refl(esk20_0,esk21_0,esk22_0) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_61]),c_0_73]),c_0_57]),c_0_58])]),c_0_55]) ).

cnf(c_0_88,plain,
    ( related_reflexive(X1,X2,X3)
    | empty_carrier(X1)
    | ~ reflexive_relstr(X1)
    | ~ element(X2,the_carrier(X1))
    | ~ element(X3,the_carrier(X1))
    | ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),the_InternalRel(X1))
    | ~ rel_str(X1) ),
    inference(spm,[status(thm)],[c_0_74,c_0_75]) ).

cnf(c_0_89,negated_conjecture,
    reflexive_relstr(poset_of_lattice(esk20_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_76]),c_0_57]),c_0_58])]) ).

cnf(c_0_90,plain,
    ( empty(X2)
    | ~ relation_of2(X1,X2,X2)
    | ~ empty_carrier(rel_str_of(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_77]) ).

cnf(c_0_91,negated_conjecture,
    relation_of2(the_InternalRel(poset_of_lattice(esk20_0)),the_carrier(esk20_0),the_carrier(esk20_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_68]),c_0_79])]) ).

cnf(c_0_92,negated_conjecture,
    rel_str_of(the_carrier(esk20_0),the_InternalRel(poset_of_lattice(esk20_0))) = poset_of_lattice(esk20_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_68]),c_0_80]),c_0_79])]) ).

cnf(c_0_93,negated_conjecture,
    ~ empty(the_carrier(esk20_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_79])]) ).

fof(c_0_94,plain,
    ! [X4,X5,X6] :
      ( ( ~ in(ordered_pair_as_product_element(the_carrier(X4),the_carrier(X4),X5,X6),relation_of_lattice(X4))
        | below_refl(X4,X5,X6)
        | ~ element(X6,the_carrier(X4))
        | ~ element(X5,the_carrier(X4))
        | empty_carrier(X4)
        | ~ lattice(X4)
        | ~ latt_str(X4) )
      & ( ~ below_refl(X4,X5,X6)
        | in(ordered_pair_as_product_element(the_carrier(X4),the_carrier(X4),X5,X6),relation_of_lattice(X4))
        | ~ element(X6,the_carrier(X4))
        | ~ element(X5,the_carrier(X4))
        | empty_carrier(X4)
        | ~ lattice(X4)
        | ~ latt_str(X4) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t32_filter_1])])])])])])]) ).

cnf(c_0_95,plain,
    ( ordered_pair_as_product_element(X1,X2,X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3))
    | empty(X2)
    | empty(X1)
    | ~ element(X4,X2)
    | ~ element(X3,X1) ),
    inference(rw,[status(thm)],[c_0_83,c_0_52]) ).

cnf(c_0_96,plain,
    ( the_InternalRel(X1) = X2
    | rel_str_of(the_carrier(X1),the_InternalRel(X1)) != rel_str_of(X3,X2)
    | ~ rel_str(X1) ),
    inference(spm,[status(thm)],[c_0_84,c_0_78]) ).

fof(c_0_97,plain,
    ! [X2] :
      ( empty_carrier(X2)
      | ~ lattice(X2)
      | ~ latt_str(X2)
      | k2_lattice3(X2) = relation_of_lattice(X2) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_k2_lattice3])])]) ).

fof(c_0_98,plain,
    ! [X4,X5,X6] :
      ( empty_carrier(X4)
      | ~ reflexive_relstr(X4)
      | ~ rel_str(X4)
      | ~ element(X5,the_carrier(X4))
      | ~ element(X6,the_carrier(X4))
      | related_reflexive(X4,X5,X5) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r3_orders_2])])])])]) ).

fof(c_0_99,plain,
    ! [X3] : element(esk7_1(X3),X3),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).

cnf(c_0_100,plain,
    ( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),the_InternalRel(X3))
    | ~ related(X3,X1,X2)
    | ~ element(X2,the_carrier(X3))
    | ~ element(X1,the_carrier(X3))
    | ~ rel_str(X3) ),
    inference(rw,[status(thm)],[c_0_85,c_0_65]) ).

cnf(c_0_101,plain,
    ( empty_carrier(X2)
    | related(X2,X3,X1)
    | ~ element(X1,the_carrier(X2))
    | ~ element(X3,the_carrier(X2))
    | ~ rel_str(X2)
    | ~ reflexive_relstr(X2)
    | ~ related_reflexive(X2,X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_63]) ).

cnf(c_0_102,negated_conjecture,
    ( related_reflexive(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk21_0),esk22_0)
    | below_refl(esk20_0,esk21_0,esk22_0) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_61]),c_0_62]),c_0_57]),c_0_58])]),c_0_55]) ).

cnf(c_0_103,negated_conjecture,
    ( empty_carrier(poset_of_lattice(esk20_0))
    | ~ below_refl(esk20_0,esk21_0,esk22_0)
    | ~ element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))
    | ~ element(esk22_0,the_carrier(poset_of_lattice(esk20_0)))
    | ~ in(unordered_pair(singleton(esk21_0),unordered_pair(esk21_0,esk22_0)),the_InternalRel(poset_of_lattice(esk20_0))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89]),c_0_79])]) ).

cnf(c_0_104,negated_conjecture,
    ~ empty_carrier(poset_of_lattice(esk20_0)),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92]),c_0_93]) ).

cnf(c_0_105,plain,
    ( empty_carrier(X1)
    | below_refl(X1,X2,X3)
    | ~ latt_str(X1)
    | ~ lattice(X1)
    | ~ element(X2,the_carrier(X1))
    | ~ element(X3,the_carrier(X1))
    | ~ in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_94]) ).

cnf(c_0_106,plain,
    ( ordered_pair_as_product_element(X1,X2,X3,X4) = unordered_pair(singleton(X3),unordered_pair(X3,X4))
    | empty(X1)
    | empty(X2)
    | ~ element(X4,X2)
    | ~ element(X3,X1) ),
    inference(rw,[status(thm)],[c_0_95,c_0_65]) ).

cnf(c_0_107,plain,
    ( the_InternalRel(X1) = X2
    | X1 != rel_str_of(X3,X2)
    | ~ strict_rel_str(X1)
    | ~ rel_str(X1) ),
    inference(spm,[status(thm)],[c_0_96,c_0_40]) ).

cnf(c_0_108,plain,
    ( k2_lattice3(X1) = relation_of_lattice(X1)
    | empty_carrier(X1)
    | ~ latt_str(X1)
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_97]) ).

cnf(c_0_109,plain,
    ( related_reflexive(X1,X2,X2)
    | empty_carrier(X1)
    | ~ element(X3,the_carrier(X1))
    | ~ element(X2,the_carrier(X1))
    | ~ rel_str(X1)
    | ~ reflexive_relstr(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_98]) ).

cnf(c_0_110,plain,
    element(esk7_1(X1),X1),
    inference(split_conjunct,[status(thm)],[c_0_99]) ).

fof(c_0_111,plain,
    ! [X3,X4] :
      ( ~ in(X3,X4)
      | element(X3,X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).

cnf(c_0_112,plain,
    ( empty_carrier(X1)
    | in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),the_InternalRel(X1))
    | ~ related_reflexive(X1,X2,X3)
    | ~ reflexive_relstr(X1)
    | ~ element(X3,the_carrier(X1))
    | ~ element(X2,the_carrier(X1))
    | ~ rel_str(X1) ),
    inference(spm,[status(thm)],[c_0_100,c_0_101]) ).

cnf(c_0_113,negated_conjecture,
    ( related_reflexive(poset_of_lattice(esk20_0),esk21_0,esk22_0)
    | below_refl(esk20_0,esk21_0,esk22_0) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_61]),c_0_73]),c_0_57]),c_0_58])]),c_0_55]) ).

cnf(c_0_114,negated_conjecture,
    ( ~ below_refl(esk20_0,esk21_0,esk22_0)
    | ~ in(unordered_pair(singleton(esk21_0),unordered_pair(esk21_0,esk22_0)),the_InternalRel(poset_of_lattice(esk20_0))) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_68]),c_0_73]),c_0_68]),c_0_62])]),c_0_104]) ).

cnf(c_0_115,plain,
    ( below_refl(X1,X2,X3)
    | empty(the_carrier(X1))
    | empty_carrier(X1)
    | ~ element(X3,the_carrier(X1))
    | ~ element(X2,the_carrier(X1))
    | ~ lattice(X1)
    | ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),relation_of_lattice(X1))
    | ~ latt_str(X1) ),
    inference(spm,[status(thm)],[c_0_105,c_0_106]) ).

cnf(c_0_116,plain,
    ( the_InternalRel(rel_str_of(X1,X2)) = X2
    | ~ strict_rel_str(rel_str_of(X1,X2))
    | ~ rel_str(rel_str_of(X1,X2)) ),
    inference(er,[status(thm)],[c_0_107]) ).

cnf(c_0_117,plain,
    ( rel_str_of(the_carrier(X1),relation_of_lattice(X1)) = poset_of_lattice(X1)
    | empty_carrier(X1)
    | ~ lattice(X1)
    | ~ latt_str(X1) ),
    inference(spm,[status(thm)],[c_0_34,c_0_108]) ).

fof(c_0_118,plain,
    ! [X3,X4] :
      ( ~ in(X3,X4)
      | ~ empty(X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).

cnf(c_0_119,plain,
    ( related_reflexive(X1,X2,X2)
    | empty_carrier(X1)
    | ~ reflexive_relstr(X1)
    | ~ element(X2,the_carrier(X1))
    | ~ rel_str(X1) ),
    inference(spm,[status(thm)],[c_0_109,c_0_110]) ).

cnf(c_0_120,plain,
    ( element(X1,X2)
    | ~ in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_111]) ).

cnf(c_0_121,plain,
    ( empty_carrier(X1)
    | in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1))
    | ~ latt_str(X1)
    | ~ lattice(X1)
    | ~ element(X2,the_carrier(X1))
    | ~ element(X3,the_carrier(X1))
    | ~ below_refl(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_94]) ).

cnf(c_0_122,negated_conjecture,
    ( below_refl(esk20_0,esk21_0,esk22_0)
    | empty_carrier(poset_of_lattice(esk20_0))
    | in(unordered_pair(singleton(esk21_0),unordered_pair(esk21_0,esk22_0)),the_InternalRel(poset_of_lattice(esk20_0)))
    | ~ element(esk22_0,the_carrier(poset_of_lattice(esk20_0)))
    | ~ element(esk21_0,the_carrier(poset_of_lattice(esk20_0))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_89]),c_0_79])]) ).

cnf(c_0_123,negated_conjecture,
    ( ~ in(unordered_pair(singleton(esk21_0),unordered_pair(esk21_0,esk22_0)),the_InternalRel(poset_of_lattice(esk20_0)))
    | ~ in(unordered_pair(singleton(esk21_0),unordered_pair(esk21_0,esk22_0)),relation_of_lattice(esk20_0)) ),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_62]),c_0_73]),c_0_57]),c_0_58])]),c_0_93]),c_0_55]) ).

cnf(c_0_124,plain,
    ( relation_of_lattice(X1) = the_InternalRel(poset_of_lattice(X1))
    | empty_carrier(X1)
    | ~ lattice(X1)
    | ~ latt_str(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_48]),c_0_49]) ).

cnf(c_0_125,plain,
    ( ~ empty(X1)
    | ~ in(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_118]) ).

cnf(c_0_126,plain,
    ( empty_carrier(X1)
    | in(unordered_pair(singleton(X2),unordered_pair(X2,X2)),the_InternalRel(X1))
    | ~ reflexive_relstr(X1)
    | ~ element(X2,the_carrier(X1))
    | ~ rel_str(X1) ),
    inference(spm,[status(thm)],[c_0_112,c_0_119]) ).

cnf(c_0_127,plain,
    ( element(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1))
    | empty_carrier(X1)
    | ~ below_refl(X1,X2,X3)
    | ~ element(X3,the_carrier(X1))
    | ~ element(X2,the_carrier(X1))
    | ~ lattice(X1)
    | ~ latt_str(X1) ),
    inference(spm,[status(thm)],[c_0_120,c_0_121]) ).

cnf(c_0_128,negated_conjecture,
    ( below_refl(esk20_0,esk21_0,esk22_0)
    | in(unordered_pair(singleton(esk21_0),unordered_pair(esk21_0,esk22_0)),the_InternalRel(poset_of_lattice(esk20_0))) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_122,c_0_68]),c_0_62]),c_0_68]),c_0_73])]),c_0_104]) ).

cnf(c_0_129,negated_conjecture,
    ~ in(unordered_pair(singleton(esk21_0),unordered_pair(esk21_0,esk22_0)),the_InternalRel(poset_of_lattice(esk20_0))),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_57]),c_0_58])]),c_0_55]) ).

cnf(c_0_130,plain,
    ( empty_carrier(X1)
    | ~ reflexive_relstr(X1)
    | ~ empty(the_InternalRel(X1))
    | ~ element(X2,the_carrier(X1))
    | ~ rel_str(X1) ),
    inference(spm,[status(thm)],[c_0_125,c_0_126]) ).

cnf(c_0_131,plain,
    ( empty(the_carrier(X1))
    | element(unordered_pair(singleton(X2),unordered_pair(X2,X3)),relation_of_lattice(X1))
    | empty_carrier(X1)
    | ~ below_refl(X1,X2,X3)
    | ~ element(X3,the_carrier(X1))
    | ~ element(X2,the_carrier(X1))
    | ~ lattice(X1)
    | ~ latt_str(X1) ),
    inference(spm,[status(thm)],[c_0_127,c_0_106]) ).

cnf(c_0_132,negated_conjecture,
    below_refl(esk20_0,esk21_0,esk22_0),
    inference(sr,[status(thm)],[c_0_128,c_0_129]) ).

fof(c_0_133,plain,
    ! [X3,X4] :
      ( ~ element(X3,X4)
      | empty(X4)
      | in(X3,X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).

cnf(c_0_134,negated_conjecture,
    ( ~ empty(the_InternalRel(poset_of_lattice(esk20_0)))
    | ~ element(X1,the_carrier(esk20_0)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_68]),c_0_89]),c_0_79])]),c_0_104]) ).

cnf(c_0_135,negated_conjecture,
    element(unordered_pair(singleton(esk21_0),unordered_pair(esk21_0,esk22_0)),relation_of_lattice(esk20_0)),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_62]),c_0_73]),c_0_57]),c_0_58])]),c_0_93]),c_0_55]) ).

cnf(c_0_136,plain,
    ( in(X1,X2)
    | empty(X2)
    | ~ element(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_133]) ).

cnf(c_0_137,negated_conjecture,
    ~ empty(the_InternalRel(poset_of_lattice(esk20_0))),
    inference(spm,[status(thm)],[c_0_134,c_0_62]) ).

cnf(c_0_138,negated_conjecture,
    element(unordered_pair(singleton(esk21_0),unordered_pair(esk21_0,esk22_0)),the_InternalRel(poset_of_lattice(esk20_0))),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_124]),c_0_57]),c_0_58])]),c_0_55]) ).

cnf(c_0_139,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_136]),c_0_137]),c_0_138])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU346+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13  % Command  : run_ET %s %d
% 0.13/0.34  % Computer : n023.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sun Jun 19 18:11:03 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.27/6.45  # Running protocol protocol_eprover_29fa5c60d0ee03ec4f64b055553dc135fbe4ee3a for 23 seconds:
% 0.27/6.45  # Preprocessing time       : 0.023 s
% 0.27/6.45  
% 0.27/6.45  # Proof found!
% 0.27/6.45  # SZS status Theorem
% 0.27/6.45  # SZS output start CNFRefutation
% See solution above
% 0.27/6.45  # Proof object total steps             : 140
% 0.27/6.45  # Proof object clause steps            : 89
% 0.27/6.45  # Proof object formula steps           : 51
% 0.27/6.45  # Proof object conjectures             : 36
% 0.27/6.45  # Proof object clause conjectures      : 33
% 0.27/6.45  # Proof object formula conjectures     : 3
% 0.27/6.45  # Proof object initial clauses used    : 37
% 0.27/6.45  # Proof object initial formulas used   : 25
% 0.27/6.45  # Proof object generating inferences   : 42
% 0.27/6.45  # Proof object simplifying inferences  : 103
% 0.27/6.45  # Training examples: 0 positive, 0 negative
% 0.27/6.45  # Parsed axioms                        : 93
% 0.27/6.45  # Removed by relevancy pruning/SinE    : 0
% 0.27/6.45  # Initial clauses                      : 182
% 0.27/6.45  # Removed in clause preprocessing      : 13
% 0.27/6.45  # Initial clauses in saturation        : 169
% 0.27/6.45  # Processed clauses                    : 12867
% 0.27/6.45  # ...of these trivial                  : 300
% 0.27/6.45  # ...subsumed                          : 9053
% 0.27/6.45  # ...remaining for further processing  : 3513
% 0.27/6.45  # Other redundant clauses eliminated   : 7
% 0.27/6.45  # Clauses deleted for lack of memory   : 53638
% 0.27/6.45  # Backward-subsumed                    : 256
% 0.27/6.45  # Backward-rewritten                   : 30
% 0.27/6.45  # Generated clauses                    : 140962
% 0.27/6.45  # ...of the previous two non-trivial   : 129897
% 0.27/6.45  # Contextual simplify-reflections      : 16383
% 0.27/6.45  # Paramodulations                      : 140817
% 0.27/6.45  # Factorizations                       : 0
% 0.27/6.45  # Equation resolutions                 : 141
% 0.27/6.45  # Current number of processed clauses  : 3225
% 0.27/6.45  #    Positive orientable unit clauses  : 107
% 0.27/6.45  #    Positive unorientable unit clauses: 1
% 0.27/6.45  #    Negative unit clauses             : 27
% 0.27/6.45  #    Non-unit-clauses                  : 3090
% 0.27/6.45  # Current number of unprocessed clauses: 57596
% 0.27/6.45  # ...number of literals in the above   : 604749
% 0.27/6.45  # Current number of archived formulas  : 0
% 0.27/6.45  # Current number of archived clauses   : 288
% 0.27/6.45  # Clause-clause subsumption calls (NU) : 10412402
% 0.27/6.45  # Rec. Clause-clause subsumption calls : 288826
% 0.27/6.45  # Non-unit clause-clause subsumptions  : 25341
% 0.27/6.45  # Unit Clause-clause subsumption calls : 18141
% 0.27/6.45  # Rewrite failures with RHS unbound    : 0
% 0.27/6.45  # BW rewrite match attempts            : 81
% 0.27/6.45  # BW rewrite match successes           : 18
% 0.27/6.45  # Condensation attempts                : 0
% 0.27/6.45  # Condensation successes               : 0
% 0.27/6.45  # Termbank termtop insertions          : 8155800
% 0.27/6.45  
% 0.27/6.45  # -------------------------------------------------
% 0.27/6.45  # User time                : 5.656 s
% 0.27/6.45  # System time              : 0.098 s
% 0.27/6.45  # Total time               : 5.754 s
% 0.27/6.45  # Maximum resident set size: 133072 pages
% 0.27/23.42  eprover: CPU time limit exceeded, terminating
% 0.27/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.44  eprover: No such file or directory
% 0.27/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.45  eprover: No such file or directory
% 0.27/23.45  eprover: CPU time limit exceeded, terminating
% 0.27/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.45  eprover: No such file or directory
% 0.27/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.ineprover: No such file or directory
% 0.27/23.46  
% 0.27/23.46  eprover: No such file or directory
% 0.27/23.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.peprover: 
% 0.27/23.47  Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.47  eprover: No such file or directory
% 0.27/23.47  eprover: No such file or directory
% 0.27/23.47  eprover: eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.pCannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.47  
% 0.27/23.47  eprover: No such file or directory
% 0.27/23.47  eprover: No such file or directory
% 0.27/23.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.48  eprover: No such file or directory
% 0.27/23.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.48  eprover: No such file or directory
% 0.27/23.49  eprover: eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.inCannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.49  
% 0.27/23.49  eprover: No such file or directory
% 0.27/23.49  eprover: No such file or directory
% 0.27/23.49  eprover: eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.inCannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.49  
% 0.27/23.49  eprover: No such file or directory
% 0.27/23.49  eprover: No such file or directory
% 0.27/23.50  eprover: eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.pCannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.50  
% 0.27/23.50  eprover: No such file or directory
% 0.27/23.50  eprover: No such file or directory
% 0.27/23.51  eprover: eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.51  Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.51  eprover: No such file or directory
% 0.27/23.51  eprover: No such file or directory
% 0.27/23.51  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.51  eprover: No such file or directory
% 0.27/23.52  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.52  eprover: No such file or directory
%------------------------------------------------------------------------------