TSTP Solution File: SEU275+1 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SEU275+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n003.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 12:39:54 EDT 2022

% Result   : Theorem 0.12s 0.34s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   55 (  28 unt;   0 def)
%            Number of atoms       :  142 (   0 equ)
%            Maximal formula atoms :   22 (   2 avg)
%            Number of connectives :  163 (  76   ~;  67   |;  11   &)
%                                         (   3 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   8 usr;   1 prp; 0-1 aty)
%            Number of functors    :    2 (   2 usr;   1 con; 0-1 aty)
%            Number of variables   :   34 (   4 sgn  26   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(d4_wellord1,axiom,
    ! [A] :
      ( relation(A)
     => ( well_ordering(A)
      <=> ( reflexive(A)
          & transitive(A)
          & antisymmetric(A)
          & connected(A)
          & well_founded_relation(A) ) ) ) ).

fof(dt_k1_wellord2,axiom,
    ! [A] : relation(inclusion_relation(A)) ).

fof(t2_wellord2,axiom,
    ! [A] : reflexive(inclusion_relation(A)) ).

fof(t3_wellord2,axiom,
    ! [A] : transitive(inclusion_relation(A)) ).

fof(t4_wellord2,axiom,
    ! [A] :
      ( ordinal(A)
     => connected(inclusion_relation(A)) ) ).

fof(t5_wellord2,axiom,
    ! [A] : antisymmetric(inclusion_relation(A)) ).

fof(t6_wellord2,axiom,
    ! [A] :
      ( ordinal(A)
     => well_founded_relation(inclusion_relation(A)) ) ).

fof(t7_wellord2,conjecture,
    ! [A] :
      ( ordinal(A)
     => well_ordering(inclusion_relation(A)) ) ).

fof(subgoal_0,plain,
    ! [A] :
      ( ordinal(A)
     => well_ordering(inclusion_relation(A)) ),
    inference(strip,[],[t7_wellord2]) ).

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

fof(normalize_0_0,plain,
    ? [A] :
      ( ~ well_ordering(inclusion_relation(A))
      & ordinal(A) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ( ~ well_ordering(inclusion_relation(skolemFOFtoCNF_A_1))
    & ordinal(skolemFOFtoCNF_A_1) ),
    inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ordinal(skolemFOFtoCNF_A_1),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [A] :
      ( ~ ordinal(A)
      | well_founded_relation(inclusion_relation(A)) ),
    inference(canonicalize,[],[t6_wellord2]) ).

fof(normalize_0_4,plain,
    ! [A] :
      ( ~ ordinal(A)
      | well_founded_relation(inclusion_relation(A)) ),
    inference(specialize,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [A] :
      ( ~ relation(A)
      | ( ~ well_ordering(A)
      <=> ( ~ antisymmetric(A)
          | ~ connected(A)
          | ~ reflexive(A)
          | ~ transitive(A)
          | ~ well_founded_relation(A) ) ) ),
    inference(canonicalize,[],[d4_wellord1]) ).

fof(normalize_0_6,plain,
    ! [A] :
      ( ~ relation(A)
      | ( ~ well_ordering(A)
      <=> ( ~ antisymmetric(A)
          | ~ connected(A)
          | ~ reflexive(A)
          | ~ transitive(A)
          | ~ well_founded_relation(A) ) ) ),
    inference(specialize,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [A] :
      ( ( ~ relation(A)
        | ~ well_ordering(A)
        | antisymmetric(A) )
      & ( ~ relation(A)
        | ~ well_ordering(A)
        | connected(A) )
      & ( ~ relation(A)
        | ~ well_ordering(A)
        | reflexive(A) )
      & ( ~ relation(A)
        | ~ well_ordering(A)
        | transitive(A) )
      & ( ~ relation(A)
        | ~ well_ordering(A)
        | well_founded_relation(A) )
      & ( ~ antisymmetric(A)
        | ~ connected(A)
        | ~ reflexive(A)
        | ~ relation(A)
        | ~ transitive(A)
        | ~ well_founded_relation(A)
        | well_ordering(A) ) ),
    inference(clausify,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    ! [A] :
      ( ~ antisymmetric(A)
      | ~ connected(A)
      | ~ reflexive(A)
      | ~ relation(A)
      | ~ transitive(A)
      | ~ well_founded_relation(A)
      | well_ordering(A) ),
    inference(conjunct,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    ! [A] : antisymmetric(inclusion_relation(A)),
    inference(canonicalize,[],[t5_wellord2]) ).

fof(normalize_0_10,plain,
    ! [A] : antisymmetric(inclusion_relation(A)),
    inference(specialize,[],[normalize_0_9]) ).

fof(normalize_0_11,plain,
    ! [A] :
      ( ~ ordinal(A)
      | connected(inclusion_relation(A)) ),
    inference(canonicalize,[],[t4_wellord2]) ).

fof(normalize_0_12,plain,
    ! [A] :
      ( ~ ordinal(A)
      | connected(inclusion_relation(A)) ),
    inference(specialize,[],[normalize_0_11]) ).

fof(normalize_0_13,plain,
    ! [A] : reflexive(inclusion_relation(A)),
    inference(canonicalize,[],[t2_wellord2]) ).

fof(normalize_0_14,plain,
    ! [A] : reflexive(inclusion_relation(A)),
    inference(specialize,[],[normalize_0_13]) ).

fof(normalize_0_15,plain,
    ! [A] : relation(inclusion_relation(A)),
    inference(canonicalize,[],[dt_k1_wellord2]) ).

fof(normalize_0_16,plain,
    ! [A] : relation(inclusion_relation(A)),
    inference(specialize,[],[normalize_0_15]) ).

fof(normalize_0_17,plain,
    ! [A] : transitive(inclusion_relation(A)),
    inference(canonicalize,[],[t3_wellord2]) ).

fof(normalize_0_18,plain,
    ! [A] : transitive(inclusion_relation(A)),
    inference(specialize,[],[normalize_0_17]) ).

fof(normalize_0_19,plain,
    ~ well_ordering(inclusion_relation(skolemFOFtoCNF_A_1)),
    inference(conjunct,[],[normalize_0_1]) ).

cnf(refute_0_0,plain,
    ordinal(skolemFOFtoCNF_A_1),
    inference(canonicalize,[],[normalize_0_2]) ).

cnf(refute_0_1,plain,
    ( ~ ordinal(A)
    | well_founded_relation(inclusion_relation(A)) ),
    inference(canonicalize,[],[normalize_0_4]) ).

cnf(refute_0_2,plain,
    ( ~ ordinal(skolemFOFtoCNF_A_1)
    | well_founded_relation(inclusion_relation(skolemFOFtoCNF_A_1)) ),
    inference(subst,[],[refute_0_1:[bind(A,$fot(skolemFOFtoCNF_A_1))]]) ).

cnf(refute_0_3,plain,
    well_founded_relation(inclusion_relation(skolemFOFtoCNF_A_1)),
    inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_A_1) )],[refute_0_0,refute_0_2]) ).

cnf(refute_0_4,plain,
    ( ~ antisymmetric(A)
    | ~ connected(A)
    | ~ reflexive(A)
    | ~ relation(A)
    | ~ transitive(A)
    | ~ well_founded_relation(A)
    | well_ordering(A) ),
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_5,plain,
    ( ~ antisymmetric(inclusion_relation(skolemFOFtoCNF_A_1))
    | ~ connected(inclusion_relation(skolemFOFtoCNF_A_1))
    | ~ reflexive(inclusion_relation(skolemFOFtoCNF_A_1))
    | ~ relation(inclusion_relation(skolemFOFtoCNF_A_1))
    | ~ transitive(inclusion_relation(skolemFOFtoCNF_A_1))
    | ~ well_founded_relation(inclusion_relation(skolemFOFtoCNF_A_1))
    | well_ordering(inclusion_relation(skolemFOFtoCNF_A_1)) ),
    inference(subst,[],[refute_0_4:[bind(A,$fot(inclusion_relation(skolemFOFtoCNF_A_1)))]]) ).

cnf(refute_0_6,plain,
    ( ~ antisymmetric(inclusion_relation(skolemFOFtoCNF_A_1))
    | ~ connected(inclusion_relation(skolemFOFtoCNF_A_1))
    | ~ reflexive(inclusion_relation(skolemFOFtoCNF_A_1))
    | ~ relation(inclusion_relation(skolemFOFtoCNF_A_1))
    | ~ transitive(inclusion_relation(skolemFOFtoCNF_A_1))
    | well_ordering(inclusion_relation(skolemFOFtoCNF_A_1)) ),
    inference(resolve,[$cnf( well_founded_relation(inclusion_relation(skolemFOFtoCNF_A_1)) )],[refute_0_3,refute_0_5]) ).

cnf(refute_0_7,plain,
    antisymmetric(inclusion_relation(A)),
    inference(canonicalize,[],[normalize_0_10]) ).

cnf(refute_0_8,plain,
    antisymmetric(inclusion_relation(skolemFOFtoCNF_A_1)),
    inference(subst,[],[refute_0_7:[bind(A,$fot(skolemFOFtoCNF_A_1))]]) ).

cnf(refute_0_9,plain,
    ( ~ connected(inclusion_relation(skolemFOFtoCNF_A_1))
    | ~ reflexive(inclusion_relation(skolemFOFtoCNF_A_1))
    | ~ relation(inclusion_relation(skolemFOFtoCNF_A_1))
    | ~ transitive(inclusion_relation(skolemFOFtoCNF_A_1))
    | well_ordering(inclusion_relation(skolemFOFtoCNF_A_1)) ),
    inference(resolve,[$cnf( antisymmetric(inclusion_relation(skolemFOFtoCNF_A_1)) )],[refute_0_8,refute_0_6]) ).

cnf(refute_0_10,plain,
    ( ~ ordinal(A)
    | connected(inclusion_relation(A)) ),
    inference(canonicalize,[],[normalize_0_12]) ).

cnf(refute_0_11,plain,
    ( ~ ordinal(skolemFOFtoCNF_A_1)
    | connected(inclusion_relation(skolemFOFtoCNF_A_1)) ),
    inference(subst,[],[refute_0_10:[bind(A,$fot(skolemFOFtoCNF_A_1))]]) ).

cnf(refute_0_12,plain,
    connected(inclusion_relation(skolemFOFtoCNF_A_1)),
    inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_A_1) )],[refute_0_0,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( ~ reflexive(inclusion_relation(skolemFOFtoCNF_A_1))
    | ~ relation(inclusion_relation(skolemFOFtoCNF_A_1))
    | ~ transitive(inclusion_relation(skolemFOFtoCNF_A_1))
    | well_ordering(inclusion_relation(skolemFOFtoCNF_A_1)) ),
    inference(resolve,[$cnf( connected(inclusion_relation(skolemFOFtoCNF_A_1)) )],[refute_0_12,refute_0_9]) ).

cnf(refute_0_14,plain,
    reflexive(inclusion_relation(A)),
    inference(canonicalize,[],[normalize_0_14]) ).

cnf(refute_0_15,plain,
    reflexive(inclusion_relation(skolemFOFtoCNF_A_1)),
    inference(subst,[],[refute_0_14:[bind(A,$fot(skolemFOFtoCNF_A_1))]]) ).

cnf(refute_0_16,plain,
    ( ~ relation(inclusion_relation(skolemFOFtoCNF_A_1))
    | ~ transitive(inclusion_relation(skolemFOFtoCNF_A_1))
    | well_ordering(inclusion_relation(skolemFOFtoCNF_A_1)) ),
    inference(resolve,[$cnf( reflexive(inclusion_relation(skolemFOFtoCNF_A_1)) )],[refute_0_15,refute_0_13]) ).

cnf(refute_0_17,plain,
    relation(inclusion_relation(A)),
    inference(canonicalize,[],[normalize_0_16]) ).

cnf(refute_0_18,plain,
    relation(inclusion_relation(skolemFOFtoCNF_A_1)),
    inference(subst,[],[refute_0_17:[bind(A,$fot(skolemFOFtoCNF_A_1))]]) ).

cnf(refute_0_19,plain,
    ( ~ transitive(inclusion_relation(skolemFOFtoCNF_A_1))
    | well_ordering(inclusion_relation(skolemFOFtoCNF_A_1)) ),
    inference(resolve,[$cnf( relation(inclusion_relation(skolemFOFtoCNF_A_1)) )],[refute_0_18,refute_0_16]) ).

cnf(refute_0_20,plain,
    transitive(inclusion_relation(A)),
    inference(canonicalize,[],[normalize_0_18]) ).

cnf(refute_0_21,plain,
    transitive(inclusion_relation(skolemFOFtoCNF_A_1)),
    inference(subst,[],[refute_0_20:[bind(A,$fot(skolemFOFtoCNF_A_1))]]) ).

cnf(refute_0_22,plain,
    well_ordering(inclusion_relation(skolemFOFtoCNF_A_1)),
    inference(resolve,[$cnf( transitive(inclusion_relation(skolemFOFtoCNF_A_1)) )],[refute_0_21,refute_0_19]) ).

cnf(refute_0_23,plain,
    ~ well_ordering(inclusion_relation(skolemFOFtoCNF_A_1)),
    inference(canonicalize,[],[normalize_0_19]) ).

cnf(refute_0_24,plain,
    $false,
    inference(resolve,[$cnf( well_ordering(inclusion_relation(skolemFOFtoCNF_A_1)) )],[refute_0_22,refute_0_23]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SEU275+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n003.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 : Sun Jun 19 03:10:13 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.34  
% 0.12/0.34  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.35  
%------------------------------------------------------------------------------