TSTP Solution File: SEU361+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SEU361+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n012.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 12:40:37 EDT 2022

% Result   : Theorem 0.18s 0.38s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   80 (  21 unt;   0 def)
%            Number of atoms       :  343 (  32 equ)
%            Maximal formula atoms :   50 (   4 avg)
%            Number of connectives :  453 ( 190   ~; 189   |;  55   &)
%                                         (   0 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   13 (  10 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-3 aty)
%            Number of variables   :   87 (   0 sgn  50   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(d11_yellow_0,axiom,
    ! [A] :
      ( rel_str(A)
     => bottom_of_relstr(A) = join_on_relstr(A,empty_set) ) ).

fof(dt_k3_yellow_0,axiom,
    ! [A] :
      ( rel_str(A)
     => element(bottom_of_relstr(A),the_carrier(A)) ) ).

fof(t30_yellow_0,axiom,
    ! [A] :
      ( ( antisymmetric_relstr(A)
        & rel_str(A) )
     => ! [B] :
          ( element(B,the_carrier(A))
         => ! [C] :
              ( ( ( B = join_on_relstr(A,C)
                  & ex_sup_of_relstr_set(A,C) )
               => ( relstr_set_smaller(A,C,B)
                  & ! [D] :
                      ( element(D,the_carrier(A))
                     => ( relstr_set_smaller(A,C,D)
                       => related(A,B,D) ) ) ) )
              & ( ( relstr_set_smaller(A,C,B)
                  & ! [D] :
                      ( element(D,the_carrier(A))
                     => ( relstr_set_smaller(A,C,D)
                       => related(A,B,D) ) ) )
               => ( B = join_on_relstr(A,C)
                  & ex_sup_of_relstr_set(A,C) ) ) ) ) ) ).

fof(t42_yellow_0,axiom,
    ! [A] :
      ( ( ~ empty_carrier(A)
        & antisymmetric_relstr(A)
        & lower_bounded_relstr(A)
        & rel_str(A) )
     => ( ex_sup_of_relstr_set(A,empty_set)
        & ex_inf_of_relstr_set(A,the_carrier(A)) ) ) ).

fof(t44_yellow_0,conjecture,
    ! [A] :
      ( ( ~ empty_carrier(A)
        & antisymmetric_relstr(A)
        & lower_bounded_relstr(A)
        & rel_str(A) )
     => ! [B] :
          ( element(B,the_carrier(A))
         => related(A,bottom_of_relstr(A),B) ) ) ).

fof(t6_yellow_0,axiom,
    ! [A] :
      ( rel_str(A)
     => ! [B] :
          ( element(B,the_carrier(A))
         => ( relstr_set_smaller(A,empty_set,B)
            & relstr_element_smaller(A,empty_set,B) ) ) ) ).

fof(subgoal_0,plain,
    ! [A] :
      ( ( ~ empty_carrier(A)
        & antisymmetric_relstr(A)
        & lower_bounded_relstr(A)
        & rel_str(A) )
     => ! [B] :
          ( element(B,the_carrier(A))
         => related(A,bottom_of_relstr(A),B) ) ),
    inference(strip,[],[t44_yellow_0]) ).

fof(negate_0_0,plain,
    ~ ! [A] :
        ( ( ~ empty_carrier(A)
          & antisymmetric_relstr(A)
          & lower_bounded_relstr(A)
          & rel_str(A) )
       => ! [B] :
            ( element(B,the_carrier(A))
           => related(A,bottom_of_relstr(A),B) ) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [A] :
      ( ~ empty_carrier(A)
      & antisymmetric_relstr(A)
      & lower_bounded_relstr(A)
      & rel_str(A)
      & ? [B] :
          ( ~ related(A,bottom_of_relstr(A),B)
          & element(B,the_carrier(A)) ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ( ~ empty_carrier(skolemFOFtoCNF_A_6)
    & antisymmetric_relstr(skolemFOFtoCNF_A_6)
    & lower_bounded_relstr(skolemFOFtoCNF_A_6)
    & rel_str(skolemFOFtoCNF_A_6)
    & ? [B] :
        ( ~ related(skolemFOFtoCNF_A_6,bottom_of_relstr(skolemFOFtoCNF_A_6),B)
        & element(B,the_carrier(skolemFOFtoCNF_A_6)) ) ),
    inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ? [B] :
      ( ~ related(skolemFOFtoCNF_A_6,bottom_of_relstr(skolemFOFtoCNF_A_6),B)
      & element(B,the_carrier(skolemFOFtoCNF_A_6)) ),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ( ~ related(skolemFOFtoCNF_A_6,bottom_of_relstr(skolemFOFtoCNF_A_6),skolemFOFtoCNF_B_1)
    & element(skolemFOFtoCNF_B_1,the_carrier(skolemFOFtoCNF_A_6)) ),
    inference(skolemize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    element(skolemFOFtoCNF_B_1,the_carrier(skolemFOFtoCNF_A_6)),
    inference(conjunct,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [A] :
      ( ~ rel_str(A)
      | ! [B] :
          ( ~ element(B,the_carrier(A))
          | ( relstr_element_smaller(A,empty_set,B)
            & relstr_set_smaller(A,empty_set,B) ) ) ),
    inference(canonicalize,[],[t6_yellow_0]) ).

fof(normalize_0_6,plain,
    ! [A] :
      ( ~ rel_str(A)
      | ! [B] :
          ( ~ element(B,the_carrier(A))
          | ( relstr_element_smaller(A,empty_set,B)
            & relstr_set_smaller(A,empty_set,B) ) ) ),
    inference(specialize,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [A,B] :
      ( ( ~ element(B,the_carrier(A))
        | ~ rel_str(A)
        | relstr_element_smaller(A,empty_set,B) )
      & ( ~ element(B,the_carrier(A))
        | ~ rel_str(A)
        | relstr_set_smaller(A,empty_set,B) ) ),
    inference(clausify,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    ! [A,B] :
      ( ~ element(B,the_carrier(A))
      | ~ rel_str(A)
      | relstr_set_smaller(A,empty_set,B) ),
    inference(conjunct,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    rel_str(skolemFOFtoCNF_A_6),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_10,plain,
    ! [A] :
      ( ~ antisymmetric_relstr(A)
      | ~ rel_str(A)
      | ! [B] :
          ( ~ element(B,the_carrier(A))
          | ( ! [C] :
                ( B != join_on_relstr(A,C)
                | ~ ex_sup_of_relstr_set(A,C)
                | ( relstr_set_smaller(A,C,B)
                  & ! [D] :
                      ( ~ element(D,the_carrier(A))
                      | ~ relstr_set_smaller(A,C,D)
                      | related(A,B,D) ) ) )
            & ! [C] :
                ( ~ relstr_set_smaller(A,C,B)
                | ( B = join_on_relstr(A,C)
                  & ex_sup_of_relstr_set(A,C) )
                | ? [D] :
                    ( ~ related(A,B,D)
                    & element(D,the_carrier(A))
                    & relstr_set_smaller(A,C,D) ) ) ) ) ),
    inference(canonicalize,[],[t30_yellow_0]) ).

fof(normalize_0_11,plain,
    ! [A] :
      ( ~ antisymmetric_relstr(A)
      | ~ rel_str(A)
      | ! [B] :
          ( ~ element(B,the_carrier(A))
          | ( ! [C] :
                ( B != join_on_relstr(A,C)
                | ~ ex_sup_of_relstr_set(A,C)
                | ( relstr_set_smaller(A,C,B)
                  & ! [D] :
                      ( ~ element(D,the_carrier(A))
                      | ~ relstr_set_smaller(A,C,D)
                      | related(A,B,D) ) ) )
            & ! [C] :
                ( ~ relstr_set_smaller(A,C,B)
                | ( B = join_on_relstr(A,C)
                  & ex_sup_of_relstr_set(A,C) )
                | ? [D] :
                    ( ~ related(A,B,D)
                    & element(D,the_carrier(A))
                    & relstr_set_smaller(A,C,D) ) ) ) ) ),
    inference(specialize,[],[normalize_0_10]) ).

fof(normalize_0_12,plain,
    ! [A,B,C,D] :
      ( ( B != join_on_relstr(A,C)
        | ~ antisymmetric_relstr(A)
        | ~ element(B,the_carrier(A))
        | ~ ex_sup_of_relstr_set(A,C)
        | ~ rel_str(A)
        | relstr_set_smaller(A,C,B) )
      & ( ~ antisymmetric_relstr(A)
        | ~ element(B,the_carrier(A))
        | ~ rel_str(A)
        | ~ related(A,B,skolemFOFtoCNF_D(A,B,C))
        | ~ relstr_set_smaller(A,C,B)
        | B = join_on_relstr(A,C) )
      & ( ~ antisymmetric_relstr(A)
        | ~ element(B,the_carrier(A))
        | ~ rel_str(A)
        | ~ related(A,B,skolemFOFtoCNF_D(A,B,C))
        | ~ relstr_set_smaller(A,C,B)
        | ex_sup_of_relstr_set(A,C) )
      & ( ~ antisymmetric_relstr(A)
        | ~ element(B,the_carrier(A))
        | ~ rel_str(A)
        | ~ relstr_set_smaller(A,C,B)
        | B = join_on_relstr(A,C)
        | element(skolemFOFtoCNF_D(A,B,C),the_carrier(A)) )
      & ( ~ antisymmetric_relstr(A)
        | ~ element(B,the_carrier(A))
        | ~ rel_str(A)
        | ~ relstr_set_smaller(A,C,B)
        | B = join_on_relstr(A,C)
        | relstr_set_smaller(A,C,skolemFOFtoCNF_D(A,B,C)) )
      & ( ~ antisymmetric_relstr(A)
        | ~ element(B,the_carrier(A))
        | ~ rel_str(A)
        | ~ relstr_set_smaller(A,C,B)
        | element(skolemFOFtoCNF_D(A,B,C),the_carrier(A))
        | ex_sup_of_relstr_set(A,C) )
      & ( ~ antisymmetric_relstr(A)
        | ~ element(B,the_carrier(A))
        | ~ rel_str(A)
        | ~ relstr_set_smaller(A,C,B)
        | ex_sup_of_relstr_set(A,C)
        | relstr_set_smaller(A,C,skolemFOFtoCNF_D(A,B,C)) )
      & ( B != join_on_relstr(A,C)
        | ~ antisymmetric_relstr(A)
        | ~ element(B,the_carrier(A))
        | ~ element(D,the_carrier(A))
        | ~ ex_sup_of_relstr_set(A,C)
        | ~ rel_str(A)
        | ~ relstr_set_smaller(A,C,D)
        | related(A,B,D) ) ),
    inference(clausify,[],[normalize_0_11]) ).

fof(normalize_0_13,plain,
    ! [A,B,C,D] :
      ( B != join_on_relstr(A,C)
      | ~ antisymmetric_relstr(A)
      | ~ element(B,the_carrier(A))
      | ~ element(D,the_carrier(A))
      | ~ ex_sup_of_relstr_set(A,C)
      | ~ rel_str(A)
      | ~ relstr_set_smaller(A,C,D)
      | related(A,B,D) ),
    inference(conjunct,[],[normalize_0_12]) ).

fof(normalize_0_14,plain,
    ! [A] :
      ( ~ rel_str(A)
      | bottom_of_relstr(A) = join_on_relstr(A,empty_set) ),
    inference(canonicalize,[],[d11_yellow_0]) ).

fof(normalize_0_15,plain,
    ! [A] :
      ( ~ rel_str(A)
      | bottom_of_relstr(A) = join_on_relstr(A,empty_set) ),
    inference(specialize,[],[normalize_0_14]) ).

fof(normalize_0_16,plain,
    antisymmetric_relstr(skolemFOFtoCNF_A_6),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_17,plain,
    ! [A] :
      ( ~ rel_str(A)
      | element(bottom_of_relstr(A),the_carrier(A)) ),
    inference(canonicalize,[],[dt_k3_yellow_0]) ).

fof(normalize_0_18,plain,
    ! [A] :
      ( ~ rel_str(A)
      | element(bottom_of_relstr(A),the_carrier(A)) ),
    inference(specialize,[],[normalize_0_17]) ).

fof(normalize_0_19,plain,
    ! [A] :
      ( ~ antisymmetric_relstr(A)
      | ~ lower_bounded_relstr(A)
      | ~ rel_str(A)
      | empty_carrier(A)
      | ( ex_inf_of_relstr_set(A,the_carrier(A))
        & ex_sup_of_relstr_set(A,empty_set) ) ),
    inference(canonicalize,[],[t42_yellow_0]) ).

fof(normalize_0_20,plain,
    ! [A] :
      ( ~ antisymmetric_relstr(A)
      | ~ lower_bounded_relstr(A)
      | ~ rel_str(A)
      | empty_carrier(A)
      | ( ex_inf_of_relstr_set(A,the_carrier(A))
        & ex_sup_of_relstr_set(A,empty_set) ) ),
    inference(specialize,[],[normalize_0_19]) ).

fof(normalize_0_21,plain,
    ! [A] :
      ( ( ~ antisymmetric_relstr(A)
        | ~ lower_bounded_relstr(A)
        | ~ rel_str(A)
        | empty_carrier(A)
        | ex_inf_of_relstr_set(A,the_carrier(A)) )
      & ( ~ antisymmetric_relstr(A)
        | ~ lower_bounded_relstr(A)
        | ~ rel_str(A)
        | empty_carrier(A)
        | ex_sup_of_relstr_set(A,empty_set) ) ),
    inference(clausify,[],[normalize_0_20]) ).

fof(normalize_0_22,plain,
    ! [A] :
      ( ~ antisymmetric_relstr(A)
      | ~ lower_bounded_relstr(A)
      | ~ rel_str(A)
      | empty_carrier(A)
      | ex_sup_of_relstr_set(A,empty_set) ),
    inference(conjunct,[],[normalize_0_21]) ).

fof(normalize_0_23,plain,
    lower_bounded_relstr(skolemFOFtoCNF_A_6),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_24,plain,
    ~ empty_carrier(skolemFOFtoCNF_A_6),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_25,plain,
    ~ related(skolemFOFtoCNF_A_6,bottom_of_relstr(skolemFOFtoCNF_A_6),skolemFOFtoCNF_B_1),
    inference(conjunct,[],[normalize_0_3]) ).

cnf(refute_0_0,plain,
    element(skolemFOFtoCNF_B_1,the_carrier(skolemFOFtoCNF_A_6)),
    inference(canonicalize,[],[normalize_0_4]) ).

cnf(refute_0_1,plain,
    ( ~ element(B,the_carrier(A))
    | ~ rel_str(A)
    | relstr_set_smaller(A,empty_set,B) ),
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_2,plain,
    ( ~ element(skolemFOFtoCNF_B_1,the_carrier(skolemFOFtoCNF_A_6))
    | ~ rel_str(skolemFOFtoCNF_A_6)
    | relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B_1) ),
    inference(subst,[],[refute_0_1:[bind(A,$fot(skolemFOFtoCNF_A_6)),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).

cnf(refute_0_3,plain,
    ( ~ rel_str(skolemFOFtoCNF_A_6)
    | relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B_1) ),
    inference(resolve,[$cnf( element(skolemFOFtoCNF_B_1,the_carrier(skolemFOFtoCNF_A_6)) )],[refute_0_0,refute_0_2]) ).

cnf(refute_0_4,plain,
    rel_str(skolemFOFtoCNF_A_6),
    inference(canonicalize,[],[normalize_0_9]) ).

cnf(refute_0_5,plain,
    relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B_1),
    inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_6) )],[refute_0_4,refute_0_3]) ).

cnf(refute_0_6,plain,
    ( B != join_on_relstr(A,C)
    | ~ antisymmetric_relstr(A)
    | ~ element(B,the_carrier(A))
    | ~ element(D,the_carrier(A))
    | ~ ex_sup_of_relstr_set(A,C)
    | ~ rel_str(A)
    | ~ relstr_set_smaller(A,C,D)
    | related(A,B,D) ),
    inference(canonicalize,[],[normalize_0_13]) ).

cnf(refute_0_7,plain,
    ( join_on_relstr(A,C) != join_on_relstr(A,C)
    | ~ antisymmetric_relstr(A)
    | ~ element(D,the_carrier(A))
    | ~ element(join_on_relstr(A,C),the_carrier(A))
    | ~ ex_sup_of_relstr_set(A,C)
    | ~ rel_str(A)
    | ~ relstr_set_smaller(A,C,D)
    | related(A,join_on_relstr(A,C),D) ),
    inference(subst,[],[refute_0_6:[bind(B,$fot(join_on_relstr(A,C)))]]) ).

cnf(refute_0_8,plain,
    join_on_relstr(A,C) = join_on_relstr(A,C),
    introduced(tautology,[refl,[$fot(join_on_relstr(A,C))]]) ).

cnf(refute_0_9,plain,
    ( ~ antisymmetric_relstr(A)
    | ~ element(D,the_carrier(A))
    | ~ element(join_on_relstr(A,C),the_carrier(A))
    | ~ ex_sup_of_relstr_set(A,C)
    | ~ rel_str(A)
    | ~ relstr_set_smaller(A,C,D)
    | related(A,join_on_relstr(A,C),D) ),
    inference(resolve,[$cnf( $equal(join_on_relstr(A,C),join_on_relstr(A,C)) )],[refute_0_8,refute_0_7]) ).

cnf(refute_0_10,plain,
    ( ~ antisymmetric_relstr(skolemFOFtoCNF_A_6)
    | ~ element(X_81,the_carrier(skolemFOFtoCNF_A_6))
    | ~ element(join_on_relstr(skolemFOFtoCNF_A_6,empty_set),the_carrier(skolemFOFtoCNF_A_6))
    | ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set)
    | ~ rel_str(skolemFOFtoCNF_A_6)
    | ~ relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,X_81)
    | related(skolemFOFtoCNF_A_6,join_on_relstr(skolemFOFtoCNF_A_6,empty_set),X_81) ),
    inference(subst,[],[refute_0_9:[bind(A,$fot(skolemFOFtoCNF_A_6)),bind(C,$fot(empty_set)),bind(D,$fot(X_81))]]) ).

cnf(refute_0_11,plain,
    ( ~ rel_str(A)
    | bottom_of_relstr(A) = join_on_relstr(A,empty_set) ),
    inference(canonicalize,[],[normalize_0_15]) ).

cnf(refute_0_12,plain,
    ( ~ rel_str(skolemFOFtoCNF_A_6)
    | bottom_of_relstr(skolemFOFtoCNF_A_6) = join_on_relstr(skolemFOFtoCNF_A_6,empty_set) ),
    inference(subst,[],[refute_0_11:[bind(A,$fot(skolemFOFtoCNF_A_6))]]) ).

cnf(refute_0_13,plain,
    bottom_of_relstr(skolemFOFtoCNF_A_6) = join_on_relstr(skolemFOFtoCNF_A_6,empty_set),
    inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_6) )],[refute_0_4,refute_0_12]) ).

cnf(refute_0_14,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_15,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_16,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_14,refute_0_15]) ).

cnf(refute_0_17,plain,
    ( bottom_of_relstr(skolemFOFtoCNF_A_6) != join_on_relstr(skolemFOFtoCNF_A_6,empty_set)
    | join_on_relstr(skolemFOFtoCNF_A_6,empty_set) = bottom_of_relstr(skolemFOFtoCNF_A_6) ),
    inference(subst,[],[refute_0_16:[bind(X,$fot(bottom_of_relstr(skolemFOFtoCNF_A_6))),bind(Y,$fot(join_on_relstr(skolemFOFtoCNF_A_6,empty_set)))]]) ).

cnf(refute_0_18,plain,
    join_on_relstr(skolemFOFtoCNF_A_6,empty_set) = bottom_of_relstr(skolemFOFtoCNF_A_6),
    inference(resolve,[$cnf( $equal(bottom_of_relstr(skolemFOFtoCNF_A_6),join_on_relstr(skolemFOFtoCNF_A_6,empty_set)) )],[refute_0_13,refute_0_17]) ).

cnf(refute_0_19,plain,
    ( join_on_relstr(skolemFOFtoCNF_A_6,empty_set) != bottom_of_relstr(skolemFOFtoCNF_A_6)
    | ~ element(bottom_of_relstr(skolemFOFtoCNF_A_6),the_carrier(skolemFOFtoCNF_A_6))
    | element(join_on_relstr(skolemFOFtoCNF_A_6,empty_set),the_carrier(skolemFOFtoCNF_A_6)) ),
    introduced(tautology,[equality,[$cnf( ~ element(join_on_relstr(skolemFOFtoCNF_A_6,empty_set),the_carrier(skolemFOFtoCNF_A_6)) ),[0],$fot(bottom_of_relstr(skolemFOFtoCNF_A_6))]]) ).

cnf(refute_0_20,plain,
    ( ~ element(bottom_of_relstr(skolemFOFtoCNF_A_6),the_carrier(skolemFOFtoCNF_A_6))
    | element(join_on_relstr(skolemFOFtoCNF_A_6,empty_set),the_carrier(skolemFOFtoCNF_A_6)) ),
    inference(resolve,[$cnf( $equal(join_on_relstr(skolemFOFtoCNF_A_6,empty_set),bottom_of_relstr(skolemFOFtoCNF_A_6)) )],[refute_0_18,refute_0_19]) ).

cnf(refute_0_21,plain,
    ( ~ antisymmetric_relstr(skolemFOFtoCNF_A_6)
    | ~ element(X_81,the_carrier(skolemFOFtoCNF_A_6))
    | ~ element(bottom_of_relstr(skolemFOFtoCNF_A_6),the_carrier(skolemFOFtoCNF_A_6))
    | ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set)
    | ~ rel_str(skolemFOFtoCNF_A_6)
    | ~ relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,X_81)
    | related(skolemFOFtoCNF_A_6,join_on_relstr(skolemFOFtoCNF_A_6,empty_set),X_81) ),
    inference(resolve,[$cnf( element(join_on_relstr(skolemFOFtoCNF_A_6,empty_set),the_carrier(skolemFOFtoCNF_A_6)) )],[refute_0_20,refute_0_10]) ).

cnf(refute_0_22,plain,
    ( join_on_relstr(skolemFOFtoCNF_A_6,empty_set) != bottom_of_relstr(skolemFOFtoCNF_A_6)
    | ~ related(skolemFOFtoCNF_A_6,join_on_relstr(skolemFOFtoCNF_A_6,empty_set),X_81)
    | related(skolemFOFtoCNF_A_6,bottom_of_relstr(skolemFOFtoCNF_A_6),X_81) ),
    introduced(tautology,[equality,[$cnf( related(skolemFOFtoCNF_A_6,join_on_relstr(skolemFOFtoCNF_A_6,empty_set),X_81) ),[1],$fot(bottom_of_relstr(skolemFOFtoCNF_A_6))]]) ).

cnf(refute_0_23,plain,
    ( ~ related(skolemFOFtoCNF_A_6,join_on_relstr(skolemFOFtoCNF_A_6,empty_set),X_81)
    | related(skolemFOFtoCNF_A_6,bottom_of_relstr(skolemFOFtoCNF_A_6),X_81) ),
    inference(resolve,[$cnf( $equal(join_on_relstr(skolemFOFtoCNF_A_6,empty_set),bottom_of_relstr(skolemFOFtoCNF_A_6)) )],[refute_0_18,refute_0_22]) ).

cnf(refute_0_24,plain,
    ( ~ antisymmetric_relstr(skolemFOFtoCNF_A_6)
    | ~ element(X_81,the_carrier(skolemFOFtoCNF_A_6))
    | ~ element(bottom_of_relstr(skolemFOFtoCNF_A_6),the_carrier(skolemFOFtoCNF_A_6))
    | ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set)
    | ~ rel_str(skolemFOFtoCNF_A_6)
    | ~ relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,X_81)
    | related(skolemFOFtoCNF_A_6,bottom_of_relstr(skolemFOFtoCNF_A_6),X_81) ),
    inference(resolve,[$cnf( related(skolemFOFtoCNF_A_6,join_on_relstr(skolemFOFtoCNF_A_6,empty_set),X_81) )],[refute_0_21,refute_0_23]) ).

cnf(refute_0_25,plain,
    antisymmetric_relstr(skolemFOFtoCNF_A_6),
    inference(canonicalize,[],[normalize_0_16]) ).

cnf(refute_0_26,plain,
    ( ~ element(X_81,the_carrier(skolemFOFtoCNF_A_6))
    | ~ element(bottom_of_relstr(skolemFOFtoCNF_A_6),the_carrier(skolemFOFtoCNF_A_6))
    | ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set)
    | ~ rel_str(skolemFOFtoCNF_A_6)
    | ~ relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,X_81)
    | related(skolemFOFtoCNF_A_6,bottom_of_relstr(skolemFOFtoCNF_A_6),X_81) ),
    inference(resolve,[$cnf( antisymmetric_relstr(skolemFOFtoCNF_A_6) )],[refute_0_25,refute_0_24]) ).

cnf(refute_0_27,plain,
    ( ~ rel_str(A)
    | element(bottom_of_relstr(A),the_carrier(A)) ),
    inference(canonicalize,[],[normalize_0_18]) ).

cnf(refute_0_28,plain,
    ( ~ rel_str(skolemFOFtoCNF_A_6)
    | element(bottom_of_relstr(skolemFOFtoCNF_A_6),the_carrier(skolemFOFtoCNF_A_6)) ),
    inference(subst,[],[refute_0_27:[bind(A,$fot(skolemFOFtoCNF_A_6))]]) ).

cnf(refute_0_29,plain,
    element(bottom_of_relstr(skolemFOFtoCNF_A_6),the_carrier(skolemFOFtoCNF_A_6)),
    inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_6) )],[refute_0_4,refute_0_28]) ).

cnf(refute_0_30,plain,
    ( ~ element(X_81,the_carrier(skolemFOFtoCNF_A_6))
    | ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set)
    | ~ rel_str(skolemFOFtoCNF_A_6)
    | ~ relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,X_81)
    | related(skolemFOFtoCNF_A_6,bottom_of_relstr(skolemFOFtoCNF_A_6),X_81) ),
    inference(resolve,[$cnf( element(bottom_of_relstr(skolemFOFtoCNF_A_6),the_carrier(skolemFOFtoCNF_A_6)) )],[refute_0_29,refute_0_26]) ).

cnf(refute_0_31,plain,
    ( ~ antisymmetric_relstr(A)
    | ~ lower_bounded_relstr(A)
    | ~ rel_str(A)
    | empty_carrier(A)
    | ex_sup_of_relstr_set(A,empty_set) ),
    inference(canonicalize,[],[normalize_0_22]) ).

cnf(refute_0_32,plain,
    ( ~ antisymmetric_relstr(skolemFOFtoCNF_A_6)
    | ~ lower_bounded_relstr(skolemFOFtoCNF_A_6)
    | ~ rel_str(skolemFOFtoCNF_A_6)
    | empty_carrier(skolemFOFtoCNF_A_6)
    | ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set) ),
    inference(subst,[],[refute_0_31:[bind(A,$fot(skolemFOFtoCNF_A_6))]]) ).

cnf(refute_0_33,plain,
    ( ~ antisymmetric_relstr(skolemFOFtoCNF_A_6)
    | ~ lower_bounded_relstr(skolemFOFtoCNF_A_6)
    | empty_carrier(skolemFOFtoCNF_A_6)
    | ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set) ),
    inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_6) )],[refute_0_4,refute_0_32]) ).

cnf(refute_0_34,plain,
    ( ~ lower_bounded_relstr(skolemFOFtoCNF_A_6)
    | empty_carrier(skolemFOFtoCNF_A_6)
    | ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set) ),
    inference(resolve,[$cnf( antisymmetric_relstr(skolemFOFtoCNF_A_6) )],[refute_0_25,refute_0_33]) ).

cnf(refute_0_35,plain,
    lower_bounded_relstr(skolemFOFtoCNF_A_6),
    inference(canonicalize,[],[normalize_0_23]) ).

cnf(refute_0_36,plain,
    ( empty_carrier(skolemFOFtoCNF_A_6)
    | ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set) ),
    inference(resolve,[$cnf( lower_bounded_relstr(skolemFOFtoCNF_A_6) )],[refute_0_35,refute_0_34]) ).

cnf(refute_0_37,plain,
    ~ empty_carrier(skolemFOFtoCNF_A_6),
    inference(canonicalize,[],[normalize_0_24]) ).

cnf(refute_0_38,plain,
    ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set),
    inference(resolve,[$cnf( empty_carrier(skolemFOFtoCNF_A_6) )],[refute_0_36,refute_0_37]) ).

cnf(refute_0_39,plain,
    ( ~ element(X_81,the_carrier(skolemFOFtoCNF_A_6))
    | ~ rel_str(skolemFOFtoCNF_A_6)
    | ~ relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,X_81)
    | related(skolemFOFtoCNF_A_6,bottom_of_relstr(skolemFOFtoCNF_A_6),X_81) ),
    inference(resolve,[$cnf( ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set) )],[refute_0_38,refute_0_30]) ).

cnf(refute_0_40,plain,
    ( ~ element(X_81,the_carrier(skolemFOFtoCNF_A_6))
    | ~ relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,X_81)
    | related(skolemFOFtoCNF_A_6,bottom_of_relstr(skolemFOFtoCNF_A_6),X_81) ),
    inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_6) )],[refute_0_4,refute_0_39]) ).

cnf(refute_0_41,plain,
    ( ~ element(skolemFOFtoCNF_B_1,the_carrier(skolemFOFtoCNF_A_6))
    | ~ relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B_1)
    | related(skolemFOFtoCNF_A_6,bottom_of_relstr(skolemFOFtoCNF_A_6),skolemFOFtoCNF_B_1) ),
    inference(subst,[],[refute_0_40:[bind(X_81,$fot(skolemFOFtoCNF_B_1))]]) ).

cnf(refute_0_42,plain,
    ( ~ element(skolemFOFtoCNF_B_1,the_carrier(skolemFOFtoCNF_A_6))
    | related(skolemFOFtoCNF_A_6,bottom_of_relstr(skolemFOFtoCNF_A_6),skolemFOFtoCNF_B_1) ),
    inference(resolve,[$cnf( relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B_1) )],[refute_0_5,refute_0_41]) ).

cnf(refute_0_43,plain,
    related(skolemFOFtoCNF_A_6,bottom_of_relstr(skolemFOFtoCNF_A_6),skolemFOFtoCNF_B_1),
    inference(resolve,[$cnf( element(skolemFOFtoCNF_B_1,the_carrier(skolemFOFtoCNF_A_6)) )],[refute_0_0,refute_0_42]) ).

cnf(refute_0_44,plain,
    ~ related(skolemFOFtoCNF_A_6,bottom_of_relstr(skolemFOFtoCNF_A_6),skolemFOFtoCNF_B_1),
    inference(canonicalize,[],[normalize_0_25]) ).

cnf(refute_0_45,plain,
    $false,
    inference(resolve,[$cnf( related(skolemFOFtoCNF_A_6,bottom_of_relstr(skolemFOFtoCNF_A_6),skolemFOFtoCNF_B_1) )],[refute_0_43,refute_0_44]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SEU361+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12  % Command  : metis --show proof --show saturation %s
% 0.11/0.33  % Computer : n012.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 600
% 0.11/0.33  % DateTime : Sun Jun 19 22:44:22 EDT 2022
% 0.11/0.33  % CPUTime  : 
% 0.11/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.38  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.38  
% 0.18/0.38  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.39  
%------------------------------------------------------------------------------