TSTP Solution File: NUM393+1 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : NUM393+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n024.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 : Mon Jul 18 12:26:23 EDT 2022

% Result   : Theorem 0.19s 0.40s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   49 (  10 unt;   0 def)
%            Number of atoms       :  137 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  152 (  64   ~;  61   |;  13   &)
%                                         (   6 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   48 (   0 sgn  34   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(connectedness_r1_ordinal1,axiom,
    ! [A,B] :
      ( ( ordinal(A)
        & ordinal(B) )
     => ( ordinal_subset(A,B)
        | ordinal_subset(B,A) ) ) ).

fof(d9_xboole_0,axiom,
    ! [A,B] :
      ( inclusion_comparable(A,B)
    <=> ( subset(A,B)
        | subset(B,A) ) ) ).

fof(redefinition_r1_ordinal1,axiom,
    ! [A,B] :
      ( ( ordinal(A)
        & ordinal(B) )
     => ( ordinal_subset(A,B)
      <=> subset(A,B) ) ) ).

fof(t25_ordinal1,conjecture,
    ! [A] :
      ( ordinal(A)
     => ! [B] :
          ( ordinal(B)
         => inclusion_comparable(A,B) ) ) ).

fof(subgoal_0,plain,
    ! [A] :
      ( ordinal(A)
     => ! [B] :
          ( ordinal(B)
         => inclusion_comparable(A,B) ) ),
    inference(strip,[],[t25_ordinal1]) ).

fof(negate_0_0,plain,
    ~ ! [A] :
        ( ordinal(A)
       => ! [B] :
            ( ordinal(B)
           => inclusion_comparable(A,B) ) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ! [A,B] :
      ( ~ inclusion_comparable(A,B)
    <=> ( ~ subset(A,B)
        & ~ subset(B,A) ) ),
    inference(canonicalize,[],[d9_xboole_0]) ).

fof(normalize_0_1,plain,
    ! [A,B] :
      ( ~ inclusion_comparable(A,B)
    <=> ( ~ subset(A,B)
        & ~ subset(B,A) ) ),
    inference(specialize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [A,B] :
      ( ( ~ subset(A,B)
        | inclusion_comparable(A,B) )
      & ( ~ subset(B,A)
        | inclusion_comparable(A,B) )
      & ( ~ inclusion_comparable(A,B)
        | subset(A,B)
        | subset(B,A) ) ),
    inference(clausify,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [A,B] :
      ( ~ subset(A,B)
      | inclusion_comparable(A,B) ),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [A,B] :
      ( ~ ordinal(A)
      | ~ ordinal(B)
      | ( ~ ordinal_subset(A,B)
      <=> ~ subset(A,B) ) ),
    inference(canonicalize,[],[redefinition_r1_ordinal1]) ).

fof(normalize_0_5,plain,
    ! [A,B] :
      ( ~ ordinal(A)
      | ~ ordinal(B)
      | ( ~ ordinal_subset(A,B)
      <=> ~ subset(A,B) ) ),
    inference(specialize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [A,B] :
      ( ( ~ ordinal(A)
        | ~ ordinal(B)
        | ~ ordinal_subset(A,B)
        | subset(A,B) )
      & ( ~ ordinal(A)
        | ~ ordinal(B)
        | ~ subset(A,B)
        | ordinal_subset(A,B) ) ),
    inference(clausify,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [A,B] :
      ( ~ ordinal(A)
      | ~ ordinal(B)
      | ~ ordinal_subset(A,B)
      | subset(A,B) ),
    inference(conjunct,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    ! [A,B] :
      ( ~ subset(B,A)
      | inclusion_comparable(A,B) ),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_9,plain,
    ? [A] :
      ( ordinal(A)
      & ? [B] :
          ( ~ inclusion_comparable(A,B)
          & ordinal(B) ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_10,plain,
    ( ordinal(skolemFOFtoCNF_A_11)
    & ? [B] :
        ( ~ inclusion_comparable(skolemFOFtoCNF_A_11,B)
        & ordinal(B) ) ),
    inference(skolemize,[],[normalize_0_9]) ).

fof(normalize_0_11,plain,
    ? [B] :
      ( ~ inclusion_comparable(skolemFOFtoCNF_A_11,B)
      & ordinal(B) ),
    inference(conjunct,[],[normalize_0_10]) ).

fof(normalize_0_12,plain,
    ( ~ inclusion_comparable(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1)
    & ordinal(skolemFOFtoCNF_B_1) ),
    inference(skolemize,[],[normalize_0_11]) ).

fof(normalize_0_13,plain,
    ordinal(skolemFOFtoCNF_B_1),
    inference(conjunct,[],[normalize_0_12]) ).

fof(normalize_0_14,plain,
    ordinal(skolemFOFtoCNF_A_11),
    inference(conjunct,[],[normalize_0_10]) ).

fof(normalize_0_15,plain,
    ! [A,B] :
      ( ~ ordinal(A)
      | ~ ordinal(B)
      | ordinal_subset(A,B)
      | ordinal_subset(B,A) ),
    inference(canonicalize,[],[connectedness_r1_ordinal1]) ).

fof(normalize_0_16,plain,
    ! [A,B] :
      ( ~ ordinal(A)
      | ~ ordinal(B)
      | ordinal_subset(A,B)
      | ordinal_subset(B,A) ),
    inference(specialize,[],[normalize_0_15]) ).

fof(normalize_0_17,plain,
    ~ inclusion_comparable(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1),
    inference(conjunct,[],[normalize_0_12]) ).

cnf(refute_0_0,plain,
    ( ~ subset(A,B)
    | inclusion_comparable(A,B) ),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_1,plain,
    ( ~ subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1)
    | inclusion_comparable(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1) ),
    inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A_11)),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).

cnf(refute_0_2,plain,
    ( ~ ordinal(A)
    | ~ ordinal(B)
    | ~ ordinal_subset(A,B)
    | subset(A,B) ),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_3,plain,
    ( ~ ordinal(skolemFOFtoCNF_A_11)
    | ~ ordinal(skolemFOFtoCNF_B_1)
    | ~ ordinal_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1)
    | subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1) ),
    inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_A_11)),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).

cnf(refute_0_4,plain,
    ( ~ subset(B,A)
    | inclusion_comparable(A,B) ),
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_5,plain,
    ( ~ subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_11)
    | inclusion_comparable(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1) ),
    inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_A_11)),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).

cnf(refute_0_6,plain,
    ordinal(skolemFOFtoCNF_B_1),
    inference(canonicalize,[],[normalize_0_13]) ).

cnf(refute_0_7,plain,
    ordinal(skolemFOFtoCNF_A_11),
    inference(canonicalize,[],[normalize_0_14]) ).

cnf(refute_0_8,plain,
    ( ~ ordinal(A)
    | ~ ordinal(B)
    | ordinal_subset(A,B)
    | ordinal_subset(B,A) ),
    inference(canonicalize,[],[normalize_0_16]) ).

cnf(refute_0_9,plain,
    ( ~ ordinal(X_68)
    | ~ ordinal(skolemFOFtoCNF_A_11)
    | ordinal_subset(X_68,skolemFOFtoCNF_A_11)
    | ordinal_subset(skolemFOFtoCNF_A_11,X_68) ),
    inference(subst,[],[refute_0_8:[bind(A,$fot(skolemFOFtoCNF_A_11)),bind(B,$fot(X_68))]]) ).

cnf(refute_0_10,plain,
    ( ~ ordinal(X_68)
    | ordinal_subset(X_68,skolemFOFtoCNF_A_11)
    | ordinal_subset(skolemFOFtoCNF_A_11,X_68) ),
    inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_A_11) )],[refute_0_7,refute_0_9]) ).

cnf(refute_0_11,plain,
    ( ~ ordinal(skolemFOFtoCNF_B_1)
    | ordinal_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1)
    | ordinal_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_11) ),
    inference(subst,[],[refute_0_10:[bind(X_68,$fot(skolemFOFtoCNF_B_1))]]) ).

cnf(refute_0_12,plain,
    ( ordinal_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1)
    | ordinal_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_11) ),
    inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_B_1) )],[refute_0_6,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( ~ ordinal(skolemFOFtoCNF_A_11)
    | ~ ordinal(skolemFOFtoCNF_B_1)
    | ~ ordinal_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_11)
    | subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_11) ),
    inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_A_11))]]) ).

cnf(refute_0_14,plain,
    ( ~ ordinal(skolemFOFtoCNF_A_11)
    | ~ ordinal(skolemFOFtoCNF_B_1)
    | ordinal_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1)
    | subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_11) ),
    inference(resolve,[$cnf( ordinal_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_11) )],[refute_0_12,refute_0_13]) ).

cnf(refute_0_15,plain,
    ( ~ ordinal(skolemFOFtoCNF_B_1)
    | ordinal_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1)
    | subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_11) ),
    inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_A_11) )],[refute_0_7,refute_0_14]) ).

cnf(refute_0_16,plain,
    ( ordinal_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1)
    | subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_11) ),
    inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_B_1) )],[refute_0_6,refute_0_15]) ).

cnf(refute_0_17,plain,
    ( inclusion_comparable(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1)
    | ordinal_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1) ),
    inference(resolve,[$cnf( subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_11) )],[refute_0_16,refute_0_5]) ).

cnf(refute_0_18,plain,
    ~ inclusion_comparable(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1),
    inference(canonicalize,[],[normalize_0_17]) ).

cnf(refute_0_19,plain,
    ordinal_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1),
    inference(resolve,[$cnf( inclusion_comparable(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1) )],[refute_0_17,refute_0_18]) ).

cnf(refute_0_20,plain,
    ( ~ ordinal(skolemFOFtoCNF_A_11)
    | ~ ordinal(skolemFOFtoCNF_B_1)
    | subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1) ),
    inference(resolve,[$cnf( ordinal_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1) )],[refute_0_19,refute_0_3]) ).

cnf(refute_0_21,plain,
    ( ~ ordinal(skolemFOFtoCNF_B_1)
    | subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1) ),
    inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_A_11) )],[refute_0_7,refute_0_20]) ).

cnf(refute_0_22,plain,
    subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1),
    inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_B_1) )],[refute_0_6,refute_0_21]) ).

cnf(refute_0_23,plain,
    inclusion_comparable(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1),
    inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1) )],[refute_0_22,refute_0_1]) ).

cnf(refute_0_24,plain,
    $false,
    inference(resolve,[$cnf( inclusion_comparable(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1) )],[refute_0_23,refute_0_18]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : NUM393+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n024.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Wed Jul  6 00:25:44 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.40  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.40  
% 0.19/0.40  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.40  
%------------------------------------------------------------------------------