TSTP Solution File: SEU369+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SEU369+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n021.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Tue Jul 19 09:19:26 EDT 2022

% Result   : Theorem 0.24s 1.42s
% Output   : CNFRefutation 0.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   83 (  14 unt;   0 def)
%            Number of atoms       :  398 (  32 equ)
%            Maximal formula atoms :   28 (   4 avg)
%            Number of connectives :  503 ( 188   ~; 207   |;  80   &)
%                                         (   6 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   34 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   32 (  30 usr;   1 prp; 0-3 aty)
%            Number of functors    :   12 (  12 usr;   3 con; 0-2 aty)
%            Number of variables   :  156 (  26 sgn  80   !;   0   ?)

% 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_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(t7_lattice3,axiom,
    ! [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(redefinition_r3_lattices,axiom,
    ! [X1,X2,X3] :
      ( ( ~ empty_carrier(X1)
        & meet_commutative(X1)
        & meet_absorbing(X1)
        & join_absorbing(X1)
        & latt_str(X1)
        & element(X2,the_carrier(X1))
        & element(X3,the_carrier(X1)) )
     => ( below_refl(X1,X2,X3)
      <=> below(X1,X2,X3) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',redefinition_r3_lattices) ).

fof(cc1_lattices,axiom,
    ! [X1] :
      ( latt_str(X1)
     => ( ( ~ empty_carrier(X1)
          & lattice(X1) )
       => ( ~ empty_carrier(X1)
          & join_commutative(X1)
          & join_associative(X1)
          & meet_commutative(X1)
          & meet_associative(X1)
          & meet_absorbing(X1)
          & join_absorbing(X1) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',cc1_lattices) ).

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(t2_lattice3,axiom,
    ! [X1,X2] :
      ( element(X2,the_carrier(boole_lattice(X1)))
     => ! [X3] :
          ( element(X3,the_carrier(boole_lattice(X1)))
         => ( below(boole_lattice(X1),X2,X3)
          <=> subset(X2,X3) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t2_lattice3) ).

fof(fc1_knaster,axiom,
    ! [X1] :
      ( ~ empty_carrier(boole_lattice(X1))
      & strict_latt_str(boole_lattice(X1))
      & join_commutative(boole_lattice(X1))
      & join_associative(boole_lattice(X1))
      & meet_commutative(boole_lattice(X1))
      & meet_associative(boole_lattice(X1))
      & meet_absorbing(boole_lattice(X1))
      & join_absorbing(boole_lattice(X1))
      & lattice(boole_lattice(X1))
      & distributive_lattstr(boole_lattice(X1))
      & modular_lattstr(boole_lattice(X1))
      & lower_bounded_semilattstr(boole_lattice(X1))
      & upper_bounded_semilattstr(boole_lattice(X1))
      & bounded_lattstr(boole_lattice(X1))
      & complemented_lattstr(boole_lattice(X1))
      & boolean_lattstr(boole_lattice(X1))
      & complete_latt_str(boole_lattice(X1)) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fc1_knaster) ).

fof(dt_k1_lattice3,axiom,
    ! [X1] :
      ( strict_latt_str(boole_lattice(X1))
      & latt_str(boole_lattice(X1)) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',dt_k1_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(t2_yellow_1,conjecture,
    ! [X1,X2] :
      ( element(X2,the_carrier(boole_POSet(X1)))
     => ! [X3] :
          ( element(X3,the_carrier(boole_POSet(X1)))
         => ( related_reflexive(boole_POSet(X1),X2,X3)
          <=> subset(X2,X3) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t2_yellow_1) ).

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(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(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(d2_yellow_1,axiom,
    ! [X1] : boole_POSet(X1) = poset_of_lattice(boole_lattice(X1)),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d2_yellow_1) ).

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(c_0_16,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_17,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])]) ).

fof(c_0_18,plain,
    ! [X4,X5,X6] :
      ( ( ~ below_refl(X4,X5,X6)
        | related_reflexive(poset_of_lattice(X4),cast_to_el_of_LattPOSet(X4,X5),cast_to_el_of_LattPOSet(X4,X6))
        | ~ element(X6,the_carrier(X4))
        | ~ element(X5,the_carrier(X4))
        | empty_carrier(X4)
        | ~ lattice(X4)
        | ~ latt_str(X4) )
      & ( ~ related_reflexive(poset_of_lattice(X4),cast_to_el_of_LattPOSet(X4,X5),cast_to_el_of_LattPOSet(X4,X6))
        | below_refl(X4,X5,X6)
        | ~ 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)],[t7_lattice3])])])])])])]) ).

fof(c_0_19,plain,
    ! [X4,X5,X6] :
      ( ( ~ below_refl(X4,X5,X6)
        | below(X4,X5,X6)
        | empty_carrier(X4)
        | ~ meet_commutative(X4)
        | ~ meet_absorbing(X4)
        | ~ join_absorbing(X4)
        | ~ latt_str(X4)
        | ~ element(X5,the_carrier(X4))
        | ~ element(X6,the_carrier(X4)) )
      & ( ~ below(X4,X5,X6)
        | below_refl(X4,X5,X6)
        | empty_carrier(X4)
        | ~ meet_commutative(X4)
        | ~ meet_absorbing(X4)
        | ~ join_absorbing(X4)
        | ~ latt_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_lattices])])])]) ).

fof(c_0_20,plain,
    ! [X2] :
      ( ( ~ empty_carrier(X2)
        | empty_carrier(X2)
        | ~ lattice(X2)
        | ~ latt_str(X2) )
      & ( join_commutative(X2)
        | empty_carrier(X2)
        | ~ lattice(X2)
        | ~ latt_str(X2) )
      & ( join_associative(X2)
        | empty_carrier(X2)
        | ~ lattice(X2)
        | ~ latt_str(X2) )
      & ( meet_commutative(X2)
        | empty_carrier(X2)
        | ~ lattice(X2)
        | ~ latt_str(X2) )
      & ( meet_associative(X2)
        | empty_carrier(X2)
        | ~ lattice(X2)
        | ~ latt_str(X2) )
      & ( meet_absorbing(X2)
        | empty_carrier(X2)
        | ~ lattice(X2)
        | ~ latt_str(X2) )
      & ( join_absorbing(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)],[cc1_lattices])])])]) ).

fof(c_0_21,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_22,plain,
    ( relation_of2(X1,X2,X3)
    | ~ relation_of2_as_subset(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_23,plain,
    ( relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1))
    | ~ rel_str(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_24,plain,
    ( empty_carrier(X1)
    | related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3))
    | ~ 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_18]) ).

cnf(c_0_25,plain,
    ( empty_carrier(X2)
    | below_refl(X2,X3,X1)
    | ~ element(X1,the_carrier(X2))
    | ~ element(X3,the_carrier(X2))
    | ~ latt_str(X2)
    | ~ join_absorbing(X2)
    | ~ meet_absorbing(X2)
    | ~ meet_commutative(X2)
    | ~ below(X2,X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_26,plain,
    ( empty_carrier(X1)
    | meet_commutative(X1)
    | ~ latt_str(X1)
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_27,plain,
    ( empty_carrier(X1)
    | meet_absorbing(X1)
    | ~ latt_str(X1)
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_28,plain,
    ( empty_carrier(X1)
    | join_absorbing(X1)
    | ~ latt_str(X1)
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

fof(c_0_29,plain,
    ! [X4,X5,X6] :
      ( ( ~ below(boole_lattice(X4),X5,X6)
        | subset(X5,X6)
        | ~ element(X6,the_carrier(boole_lattice(X4)))
        | ~ element(X5,the_carrier(boole_lattice(X4))) )
      & ( ~ subset(X5,X6)
        | below(boole_lattice(X4),X5,X6)
        | ~ element(X6,the_carrier(boole_lattice(X4)))
        | ~ element(X5,the_carrier(boole_lattice(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)],[t2_lattice3])])])])])]) ).

fof(c_0_30,plain,
    ! [X2,X2,X2,X2,X2,X2,X2,X2,X2,X2,X2,X2,X2,X2,X2,X2,X2] :
      ( ~ empty_carrier(boole_lattice(X2))
      & strict_latt_str(boole_lattice(X2))
      & join_commutative(boole_lattice(X2))
      & join_associative(boole_lattice(X2))
      & meet_commutative(boole_lattice(X2))
      & meet_associative(boole_lattice(X2))
      & meet_absorbing(boole_lattice(X2))
      & join_absorbing(boole_lattice(X2))
      & lattice(boole_lattice(X2))
      & distributive_lattstr(boole_lattice(X2))
      & modular_lattstr(boole_lattice(X2))
      & lower_bounded_semilattstr(boole_lattice(X2))
      & upper_bounded_semilattstr(boole_lattice(X2))
      & bounded_lattstr(boole_lattice(X2))
      & complemented_lattstr(boole_lattice(X2))
      & boolean_lattstr(boole_lattice(X2))
      & complete_latt_str(boole_lattice(X2)) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fc1_knaster])])])]) ).

fof(c_0_31,plain,
    ! [X2,X2] :
      ( strict_latt_str(boole_lattice(X2))
      & latt_str(boole_lattice(X2)) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[dt_k1_lattice3])])]) ).

cnf(c_0_32,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_21]) ).

cnf(c_0_33,plain,
    ( relation_of2(the_InternalRel(X1),the_carrier(X1),the_carrier(X1))
    | ~ rel_str(X1) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

fof(c_0_34,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])]) ).

cnf(c_0_35,plain,
    ( empty_carrier(X2)
    | below(X2,X3,X1)
    | ~ element(X1,the_carrier(X2))
    | ~ element(X3,the_carrier(X2))
    | ~ latt_str(X2)
    | ~ join_absorbing(X2)
    | ~ meet_absorbing(X2)
    | ~ meet_commutative(X2)
    | ~ below_refl(X2,X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_36,plain,
    ( empty_carrier(X1)
    | below_refl(X1,X2,X3)
    | ~ latt_str(X1)
    | ~ lattice(X1)
    | ~ element(X2,the_carrier(X1))
    | ~ element(X3,the_carrier(X1))
    | ~ related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

fof(c_0_37,negated_conjecture,
    ~ ! [X1,X2] :
        ( element(X2,the_carrier(boole_POSet(X1)))
       => ! [X3] :
            ( element(X3,the_carrier(boole_POSet(X1)))
           => ( related_reflexive(boole_POSet(X1),X2,X3)
            <=> subset(X2,X3) ) ) ),
    inference(assume_negation,[status(cth)],[t2_yellow_1]) ).

cnf(c_0_38,plain,
    ( related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3))
    | empty_carrier(X1)
    | ~ below(X1,X2,X3)
    | ~ element(X3,the_carrier(X1))
    | ~ element(X2,the_carrier(X1))
    | ~ lattice(X1)
    | ~ latt_str(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27]),c_0_28]) ).

cnf(c_0_39,plain,
    ( below(boole_lattice(X2),X1,X3)
    | ~ element(X1,the_carrier(boole_lattice(X2)))
    | ~ element(X3,the_carrier(boole_lattice(X2)))
    | ~ subset(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_40,plain,
    lattice(boole_lattice(X1)),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_41,plain,
    latt_str(boole_lattice(X1)),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_42,plain,
    ~ empty_carrier(boole_lattice(X1)),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

fof(c_0_43,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_44,plain,
    ( the_carrier(X1) = X2
    | rel_str_of(the_carrier(X1),the_InternalRel(X1)) != rel_str_of(X2,X3)
    | ~ rel_str(X1) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_45,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_34]) ).

fof(c_0_46,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])])]) ).

fof(c_0_47,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])])]) ).

cnf(c_0_48,plain,
    ( subset(X1,X3)
    | ~ element(X1,the_carrier(boole_lattice(X2)))
    | ~ element(X3,the_carrier(boole_lattice(X2)))
    | ~ below(boole_lattice(X2),X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_49,plain,
    ( below(X1,X2,X3)
    | empty_carrier(X1)
    | ~ related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3))
    | ~ element(X2,the_carrier(X1))
    | ~ element(X3,the_carrier(X1))
    | ~ lattice(X1)
    | ~ latt_str(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_26]),c_0_27]),c_0_28]) ).

fof(c_0_50,negated_conjecture,
    ( element(esk30_0,the_carrier(boole_POSet(esk29_0)))
    & element(esk31_0,the_carrier(boole_POSet(esk29_0)))
    & ( ~ related_reflexive(boole_POSet(esk29_0),esk30_0,esk31_0)
      | ~ subset(esk30_0,esk31_0) )
    & ( related_reflexive(boole_POSet(esk29_0),esk30_0,esk31_0)
      | subset(esk30_0,esk31_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)],[c_0_37])])])])]) ).

fof(c_0_51,plain,
    ! [X2] : boole_POSet(X2) = poset_of_lattice(boole_lattice(X2)),
    inference(variable_rename,[status(thm)],[d2_yellow_1]) ).

cnf(c_0_52,plain,
    ( related_reflexive(poset_of_lattice(boole_lattice(X1)),cast_to_el_of_LattPOSet(boole_lattice(X1),X2),cast_to_el_of_LattPOSet(boole_lattice(X1),X3))
    | ~ subset(X2,X3)
    | ~ element(X3,the_carrier(boole_lattice(X1)))
    | ~ element(X2,the_carrier(boole_lattice(X1))) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_41])]),c_0_42]) ).

cnf(c_0_53,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_43]) ).

cnf(c_0_54,plain,
    ( the_carrier(X1) = X2
    | X1 != rel_str_of(X2,X3)
    | ~ strict_rel_str(X1)
    | ~ rel_str(X1) ),
    inference(spm,[status(thm)],[c_0_44,c_0_45]) ).

cnf(c_0_55,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_46]) ).

cnf(c_0_56,plain,
    ( k2_lattice3(X1) = relation_of_lattice(X1)
    | empty_carrier(X1)
    | ~ latt_str(X1)
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_47]) ).

fof(c_0_57,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])])])]) ).

cnf(c_0_58,plain,
    ( subset(X1,X2)
    | ~ related_reflexive(poset_of_lattice(boole_lattice(X3)),cast_to_el_of_LattPOSet(boole_lattice(X3),X1),cast_to_el_of_LattPOSet(boole_lattice(X3),X2))
    | ~ element(X2,the_carrier(boole_lattice(X3)))
    | ~ element(X1,the_carrier(boole_lattice(X3))) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_40]),c_0_41])]),c_0_42]) ).

cnf(c_0_59,negated_conjecture,
    ( ~ subset(esk30_0,esk31_0)
    | ~ related_reflexive(boole_POSet(esk29_0),esk30_0,esk31_0) ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

cnf(c_0_60,plain,
    boole_POSet(X1) = poset_of_lattice(boole_lattice(X1)),
    inference(split_conjunct,[status(thm)],[c_0_51]) ).

cnf(c_0_61,plain,
    ( related_reflexive(poset_of_lattice(boole_lattice(X1)),cast_to_el_of_LattPOSet(boole_lattice(X1),X2),X3)
    | ~ subset(X2,X3)
    | ~ element(X3,the_carrier(boole_lattice(X1)))
    | ~ element(X2,the_carrier(boole_lattice(X1))) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_40]),c_0_41])]),c_0_42]) ).

cnf(c_0_62,plain,
    ( the_carrier(rel_str_of(X1,X2)) = X1
    | ~ strict_rel_str(rel_str_of(X1,X2))
    | ~ rel_str(rel_str_of(X1,X2)) ),
    inference(er,[status(thm)],[c_0_54]) ).

cnf(c_0_63,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_55,c_0_56]) ).

cnf(c_0_64,plain,
    ( empty_carrier(X1)
    | rel_str(poset_of_lattice(X1))
    | ~ latt_str(X1)
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_57]) ).

cnf(c_0_65,plain,
    ( empty_carrier(X1)
    | strict_rel_str(poset_of_lattice(X1))
    | ~ latt_str(X1)
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_57]) ).

cnf(c_0_66,plain,
    ( subset(X1,X2)
    | ~ related_reflexive(poset_of_lattice(boole_lattice(X3)),cast_to_el_of_LattPOSet(boole_lattice(X3),X1),X2)
    | ~ element(X2,the_carrier(boole_lattice(X3)))
    | ~ element(X1,the_carrier(boole_lattice(X3))) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_53]),c_0_40]),c_0_41])]),c_0_42]) ).

cnf(c_0_67,negated_conjecture,
    ( subset(esk30_0,esk31_0)
    | related_reflexive(boole_POSet(esk29_0),esk30_0,esk31_0) ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

cnf(c_0_68,negated_conjecture,
    ( ~ subset(esk30_0,esk31_0)
    | ~ related_reflexive(poset_of_lattice(boole_lattice(esk29_0)),esk30_0,esk31_0) ),
    inference(rw,[status(thm)],[c_0_59,c_0_60]) ).

cnf(c_0_69,plain,
    ( related_reflexive(poset_of_lattice(boole_lattice(X1)),X2,X3)
    | ~ subset(X2,X3)
    | ~ element(X3,the_carrier(boole_lattice(X1)))
    | ~ element(X2,the_carrier(boole_lattice(X1))) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_53]),c_0_40]),c_0_41])]),c_0_42]) ).

cnf(c_0_70,negated_conjecture,
    element(esk31_0,the_carrier(boole_POSet(esk29_0))),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

cnf(c_0_71,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(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]),c_0_65]) ).

cnf(c_0_72,plain,
    ( subset(X1,X2)
    | ~ related_reflexive(poset_of_lattice(boole_lattice(X3)),X1,X2)
    | ~ element(X2,the_carrier(boole_lattice(X3)))
    | ~ element(X1,the_carrier(boole_lattice(X3))) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_53]),c_0_40]),c_0_41])]),c_0_42]) ).

cnf(c_0_73,negated_conjecture,
    ( subset(esk30_0,esk31_0)
    | related_reflexive(poset_of_lattice(boole_lattice(esk29_0)),esk30_0,esk31_0) ),
    inference(rw,[status(thm)],[c_0_67,c_0_60]) ).

cnf(c_0_74,negated_conjecture,
    ( ~ subset(esk30_0,esk31_0)
    | ~ element(esk31_0,the_carrier(boole_lattice(esk29_0)))
    | ~ element(esk30_0,the_carrier(boole_lattice(esk29_0))) ),
    inference(spm,[status(thm)],[c_0_68,c_0_69]) ).

cnf(c_0_75,negated_conjecture,
    element(esk31_0,the_carrier(poset_of_lattice(boole_lattice(esk29_0)))),
    inference(rw,[status(thm)],[c_0_70,c_0_60]) ).

cnf(c_0_76,plain,
    the_carrier(poset_of_lattice(boole_lattice(X1))) = the_carrier(boole_lattice(X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_71]),c_0_40]),c_0_41])]) ).

cnf(c_0_77,negated_conjecture,
    element(esk30_0,the_carrier(boole_POSet(esk29_0))),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

cnf(c_0_78,negated_conjecture,
    ( ~ element(esk31_0,the_carrier(boole_lattice(esk29_0)))
    | ~ element(esk30_0,the_carrier(boole_lattice(esk29_0))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]) ).

cnf(c_0_79,negated_conjecture,
    element(esk31_0,the_carrier(boole_lattice(esk29_0))),
    inference(rw,[status(thm)],[c_0_75,c_0_76]) ).

cnf(c_0_80,negated_conjecture,
    element(esk30_0,the_carrier(poset_of_lattice(boole_lattice(esk29_0)))),
    inference(rw,[status(thm)],[c_0_77,c_0_60]) ).

cnf(c_0_81,negated_conjecture,
    ~ element(esk30_0,the_carrier(boole_lattice(esk29_0))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_79])]) ).

cnf(c_0_82,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_76]),c_0_81]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SEU369+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.12  % Command  : run_ET %s %d
% 0.13/0.33  % Computer : n021.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sun Jun 19 19:46:18 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.24/1.42  # Running protocol protocol_eprover_29fa5c60d0ee03ec4f64b055553dc135fbe4ee3a for 23 seconds:
% 0.24/1.42  # Preprocessing time       : 0.027 s
% 0.24/1.42  
% 0.24/1.42  # Proof found!
% 0.24/1.42  # SZS status Theorem
% 0.24/1.42  # SZS output start CNFRefutation
% See solution above
% 0.24/1.42  # Proof object total steps             : 83
% 0.24/1.42  # Proof object clause steps            : 50
% 0.24/1.42  # Proof object formula steps           : 33
% 0.24/1.42  # Proof object conjectures             : 16
% 0.24/1.42  # Proof object clause conjectures      : 13
% 0.24/1.42  # Proof object formula conjectures     : 3
% 0.24/1.42  # Proof object initial clauses used    : 26
% 0.24/1.42  # Proof object initial formulas used   : 16
% 0.24/1.42  # Proof object generating inferences   : 17
% 0.24/1.42  # Proof object simplifying inferences  : 45
% 0.24/1.42  # Training examples: 0 positive, 0 negative
% 0.24/1.42  # Parsed axioms                        : 121
% 0.24/1.42  # Removed by relevancy pruning/SinE    : 0
% 0.24/1.42  # Initial clauses                      : 402
% 0.24/1.42  # Removed in clause preprocessing      : 26
% 0.24/1.42  # Initial clauses in saturation        : 376
% 0.24/1.42  # Processed clauses                    : 1386
% 0.24/1.42  # ...of these trivial                  : 50
% 0.24/1.42  # ...subsumed                          : 183
% 0.24/1.42  # ...remaining for further processing  : 1152
% 0.24/1.42  # Other redundant clauses eliminated   : 5
% 0.24/1.42  # Clauses deleted for lack of memory   : 0
% 0.24/1.42  # Backward-subsumed                    : 13
% 0.24/1.42  # Backward-rewritten                   : 23
% 0.24/1.42  # Generated clauses                    : 3904
% 0.24/1.42  # ...of the previous two non-trivial   : 3686
% 0.24/1.42  # Contextual simplify-reflections      : 161
% 0.24/1.42  # Paramodulations                      : 3877
% 0.24/1.42  # Factorizations                       : 0
% 0.24/1.42  # Equation resolutions                 : 24
% 0.24/1.42  # Current number of processed clauses  : 1115
% 0.24/1.42  #    Positive orientable unit clauses  : 242
% 0.24/1.42  #    Positive unorientable unit clauses: 1
% 0.24/1.42  #    Negative unit clauses             : 26
% 0.24/1.42  #    Non-unit-clauses                  : 846
% 0.24/1.42  # Current number of unprocessed clauses: 2586
% 0.24/1.42  # ...number of literals in the above   : 14925
% 0.24/1.42  # Current number of archived formulas  : 0
% 0.24/1.42  # Current number of archived clauses   : 38
% 0.24/1.42  # Clause-clause subsumption calls (NU) : 241645
% 0.24/1.42  # Rec. Clause-clause subsumption calls : 60770
% 0.24/1.42  # Non-unit clause-clause subsumptions  : 316
% 0.24/1.42  # Unit Clause-clause subsumption calls : 5275
% 0.24/1.42  # Rewrite failures with RHS unbound    : 0
% 0.24/1.42  # BW rewrite match attempts            : 41
% 0.24/1.42  # BW rewrite match successes           : 8
% 0.24/1.42  # Condensation attempts                : 0
% 0.24/1.42  # Condensation successes               : 0
% 0.24/1.42  # Termbank termtop insertions          : 97186
% 0.24/1.42  
% 0.24/1.42  # -------------------------------------------------
% 0.24/1.42  # User time                : 0.181 s
% 0.24/1.42  # System time              : 0.005 s
% 0.24/1.42  # Total time               : 0.186 s
% 0.24/1.42  # Maximum resident set size: 9116 pages
% 0.24/23.41  eprover: CPU time limit exceeded, terminating
% 0.24/23.43  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.43  eprover: No such file or directory
% 0.24/23.43  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.43  eprover: No such file or directory
% 0.24/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.44  eprover: No such file or directory
% 0.24/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.44  eprover: No such file or directory
% 0.24/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.45  eprover: No such file or directory
% 0.24/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.46  eprover: No such file or directory
% 0.24/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.46  eprover: No such file or directory
% 0.24/23.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.47  eprover: No such file or directory
% 0.24/23.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.47  eprover: No such file or directory
% 0.24/23.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.48  eprover: No such file or directory
% 0.24/23.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.48  eprover: No such file or directory
%------------------------------------------------------------------------------