TSTP Solution File: SEU173+1 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SEU173+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n027.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 12:39:02 EDT 2022

% Result   : Theorem 0.13s 0.35s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   40 (  13 unt;   0 def)
%            Number of atoms       :  107 (  11 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  116 (  49   ~;  32   |;  11   &)
%                                         (  15 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   66 (   1 sgn  47   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(d1_zfmisc_1,axiom,
    ! [A,B] :
      ( B = powerset(A)
    <=> ! [C] :
          ( in(C,B)
        <=> subset(C,A) ) ) ).

fof(d2_subset_1,axiom,
    ! [A,B] :
      ( ( ~ empty(A)
       => ( element(B,A)
        <=> in(B,A) ) )
      & ( empty(A)
       => ( element(B,A)
        <=> empty(B) ) ) ) ).

fof(d3_tarski,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( in(C,A)
         => in(C,B) ) ) ).

fof(fc1_subset_1,axiom,
    ! [A] : ~ empty(powerset(A)) ).

fof(l71_subset_1,conjecture,
    ! [A,B] :
      ( ! [C] :
          ( in(C,A)
         => in(C,B) )
     => element(A,powerset(B)) ) ).

fof(subgoal_0,plain,
    ! [A,B] :
      ( ! [C] :
          ( in(C,A)
         => in(C,B) )
     => element(A,powerset(B)) ),
    inference(strip,[],[l71_subset_1]) ).

fof(negate_0_0,plain,
    ~ ! [A,B] :
        ( ! [C] :
            ( in(C,A)
           => in(C,B) )
       => element(A,powerset(B)) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [A,B] :
      ( ~ element(A,powerset(B))
      & ! [C] :
          ( ~ in(C,A)
          | in(C,B) ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ! [A,B] :
      ( ~ subset(A,B)
    <=> ? [C] :
          ( ~ in(C,B)
          & in(C,A) ) ),
    inference(canonicalize,[],[d3_tarski]) ).

fof(normalize_0_2,plain,
    ! [A,B] :
      ( ~ subset(A,B)
    <=> ? [C] :
          ( ~ in(C,B)
          & in(C,A) ) ),
    inference(specialize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ? [A,B] :
      ( ~ element(A,powerset(B))
      & subset(A,B) ),
    inference(simplify,[],[normalize_0_0,normalize_0_2]) ).

fof(normalize_0_4,plain,
    ( ~ element(skolemFOFtoCNF_A_2,powerset(skolemFOFtoCNF_B_3))
    & subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3) ),
    inference(skolemize,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3),
    inference(conjunct,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [A,B] :
      ( B != powerset(A)
    <=> ? [C] :
          ( ~ in(C,B)
        <=> subset(C,A) ) ),
    inference(canonicalize,[],[d1_zfmisc_1]) ).

fof(normalize_0_7,plain,
    ! [A,B] :
      ( B != powerset(A)
    <=> ? [C] :
          ( ~ in(C,B)
        <=> subset(C,A) ) ),
    inference(specialize,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    ! [A,B,C] :
      ( ( B != powerset(A)
        | ~ in(C,B)
        | subset(C,A) )
      & ( B != powerset(A)
        | ~ subset(C,A)
        | in(C,B) )
      & ( ~ in(skolemFOFtoCNF_C(A,B),B)
        | ~ subset(skolemFOFtoCNF_C(A,B),A)
        | B = powerset(A) )
      & ( B = powerset(A)
        | in(skolemFOFtoCNF_C(A,B),B)
        | subset(skolemFOFtoCNF_C(A,B),A) ) ),
    inference(clausify,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    ! [A,B,C] :
      ( B != powerset(A)
      | ~ subset(C,A)
      | in(C,B) ),
    inference(conjunct,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ( ! [A] :
        ( ~ empty(A)
        | ! [B] :
            ( ~ element(B,A)
          <=> ~ empty(B) ) )
    & ! [A] :
        ( empty(A)
        | ! [B] :
            ( ~ element(B,A)
          <=> ~ in(B,A) ) ) ),
    inference(canonicalize,[],[d2_subset_1]) ).

fof(normalize_0_11,plain,
    ! [A] :
      ( empty(A)
      | ! [B] :
          ( ~ element(B,A)
        <=> ~ in(B,A) ) ),
    inference(conjunct,[],[normalize_0_10]) ).

fof(normalize_0_12,plain,
    ! [A] :
      ( empty(A)
      | ! [B] :
          ( ~ element(B,A)
        <=> ~ in(B,A) ) ),
    inference(specialize,[],[normalize_0_11]) ).

fof(normalize_0_13,plain,
    ! [A,B] :
      ( ( ~ element(B,A)
        | empty(A)
        | in(B,A) )
      & ( ~ in(B,A)
        | element(B,A)
        | empty(A) ) ),
    inference(clausify,[],[normalize_0_12]) ).

fof(normalize_0_14,plain,
    ! [A,B] :
      ( ~ in(B,A)
      | element(B,A)
      | empty(A) ),
    inference(conjunct,[],[normalize_0_13]) ).

fof(normalize_0_15,plain,
    ~ element(skolemFOFtoCNF_A_2,powerset(skolemFOFtoCNF_B_3)),
    inference(conjunct,[],[normalize_0_4]) ).

fof(normalize_0_16,plain,
    ! [A] : ~ empty(powerset(A)),
    inference(canonicalize,[],[fc1_subset_1]) ).

fof(normalize_0_17,plain,
    ! [A] : ~ empty(powerset(A)),
    inference(specialize,[],[normalize_0_16]) ).

cnf(refute_0_0,plain,
    subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_1,plain,
    ( B != powerset(A)
    | ~ subset(C,A)
    | in(C,B) ),
    inference(canonicalize,[],[normalize_0_9]) ).

cnf(refute_0_2,plain,
    ( powerset(A) != powerset(A)
    | ~ subset(C,A)
    | in(C,powerset(A)) ),
    inference(subst,[],[refute_0_1:[bind(B,$fot(powerset(A)))]]) ).

cnf(refute_0_3,plain,
    powerset(A) = powerset(A),
    introduced(tautology,[refl,[$fot(powerset(A))]]) ).

cnf(refute_0_4,plain,
    ( ~ subset(C,A)
    | in(C,powerset(A)) ),
    inference(resolve,[$cnf( $equal(powerset(A),powerset(A)) )],[refute_0_3,refute_0_2]) ).

cnf(refute_0_5,plain,
    ( ~ subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3)
    | in(skolemFOFtoCNF_A_2,powerset(skolemFOFtoCNF_B_3)) ),
    inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_B_3)),bind(C,$fot(skolemFOFtoCNF_A_2))]]) ).

cnf(refute_0_6,plain,
    in(skolemFOFtoCNF_A_2,powerset(skolemFOFtoCNF_B_3)),
    inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_3) )],[refute_0_0,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( ~ in(B,A)
    | element(B,A)
    | empty(A) ),
    inference(canonicalize,[],[normalize_0_14]) ).

cnf(refute_0_8,plain,
    ( ~ in(skolemFOFtoCNF_A_2,powerset(skolemFOFtoCNF_B_3))
    | element(skolemFOFtoCNF_A_2,powerset(skolemFOFtoCNF_B_3))
    | empty(powerset(skolemFOFtoCNF_B_3)) ),
    inference(subst,[],[refute_0_7:[bind(A,$fot(powerset(skolemFOFtoCNF_B_3))),bind(B,$fot(skolemFOFtoCNF_A_2))]]) ).

cnf(refute_0_9,plain,
    ( element(skolemFOFtoCNF_A_2,powerset(skolemFOFtoCNF_B_3))
    | empty(powerset(skolemFOFtoCNF_B_3)) ),
    inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,powerset(skolemFOFtoCNF_B_3)) )],[refute_0_6,refute_0_8]) ).

cnf(refute_0_10,plain,
    ~ element(skolemFOFtoCNF_A_2,powerset(skolemFOFtoCNF_B_3)),
    inference(canonicalize,[],[normalize_0_15]) ).

cnf(refute_0_11,plain,
    empty(powerset(skolemFOFtoCNF_B_3)),
    inference(resolve,[$cnf( element(skolemFOFtoCNF_A_2,powerset(skolemFOFtoCNF_B_3)) )],[refute_0_9,refute_0_10]) ).

cnf(refute_0_12,plain,
    ~ empty(powerset(A)),
    inference(canonicalize,[],[normalize_0_17]) ).

cnf(refute_0_13,plain,
    ~ empty(powerset(skolemFOFtoCNF_B_3)),
    inference(subst,[],[refute_0_12:[bind(A,$fot(skolemFOFtoCNF_B_3))]]) ).

cnf(refute_0_14,plain,
    $false,
    inference(resolve,[$cnf( empty(powerset(skolemFOFtoCNF_B_3)) )],[refute_0_11,refute_0_13]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : SEU173+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12  % Command  : metis --show proof --show saturation %s
% 0.13/0.33  % Computer : n027.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
% 0.13/0.33  % DateTime : Sun Jun 19 16:29:39 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35  
% 0.13/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.35  
%------------------------------------------------------------------------------