TSTP Solution File: SEU820^2 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU820^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n028.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  : 300s
% DateTime : Tue May 21 03:43:57 EDT 2024

% Result   : Theorem 6.27s 2.64s
% Output   : Refutation 6.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   64 (  14 unt;  16 typ;   4 def)
%            Number of atoms       :  146 (  21 equ;   0 cnn)
%            Maximal formula atoms :   26 (   3 avg)
%            Number of connectives :  275 (  47   ~;  55   |;   7   &; 140   @)
%                                         (   0 <=>;  26  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   20 (  18 usr;  15 con; 0-2 aty)
%            Number of variables   :   39 (   1   ^  37   !;   1   ?;  39   :)

% Comments : 
%------------------------------------------------------------------------------
thf(in_type,type,
    in: $i > $i > $o ).

thf(emptyset_type,type,
    emptyset: $i ).

thf(powerset_type,type,
    powerset: $i > $i ).

thf(vacuousDall_type,type,
    vacuousDall: $o ).

thf(vacuousDall_def,definition,
    ( vacuousDall
    = ( ! [A: $i > $o,B: $i] :
          ( ( in @ B @ emptyset )
         => ( A @ B ) ) ) ) ).

thf(subset_type,type,
    subset: $i > $i > $o ).

thf(subsetemptysetimpeq_type,type,
    subsetemptysetimpeq: $o ).

thf(subsetemptysetimpeq_def,definition,
    ( subsetemptysetimpeq
    = ( ! [A: $i] :
          ( ( subset @ A @ emptyset )
         => ( A = emptyset ) ) ) ) ).

thf(powersetE1_type,type,
    powersetE1: $o ).

thf(powersetE1_def,definition,
    ( powersetE1
    = ( ! [A: $i,B: $i] :
          ( ( in @ B @ ( powerset @ A ) )
         => ( subset @ B @ A ) ) ) ) ).

thf(ordinal_type,type,
    ordinal: $i > $o ).

thf(ordinal_def,definition,
    ( ordinal
    = ( ^ [A: $i] :
          ( ( transitiveset @ A )
          & ( wellorderedByIn @ A ) ) ) ) ).

thf(sk1_type,type,
    sk1: $o ).

thf(sk2_type,type,
    sk2: $i ).

thf(sk3_type,type,
    sk3: $o ).

thf(sk4_type,type,
    sk4: $o ).

thf(sk7_type,type,
    sk7: $i ).

thf(sk8_type,type,
    sk8: $i ).

thf(sk10_type,type,
    sk10: $i ).

thf(sk11_type,type,
    sk11: $i ).

thf(1,conjecture,
    ( vacuousDall
   => ( subsetemptysetimpeq
     => ( powersetE1
       => ( ordinal @ emptyset ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetOrdinal) ).

thf(2,negated_conjecture,
    ~ ( vacuousDall
     => ( subsetemptysetimpeq
       => ( powersetE1
         => ( ordinal @ emptyset ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ! [A: $i > $o,B: $i] :
          ( ( in @ B @ emptyset )
         => ( A @ B ) )
     => ( ! [A: $i] :
            ( ( subset @ A @ emptyset )
           => ( A = emptyset ) )
       => ( ! [A: $i,B: $i] :
              ( ( in @ B @ ( powerset @ A ) )
             => ( subset @ B @ A ) )
         => ( ! [A: $i] :
                ( ( in @ A @ emptyset )
               => ( subset @ A @ emptyset ) )
            & ! [A: $i] :
                ( ( in @ A @ emptyset )
               => ! [B: $i] :
                    ( ( in @ B @ emptyset )
                   => ! [C: $i] :
                        ( ( in @ C @ emptyset )
                       => ( ( ( in @ A @ B )
                            & ( in @ B @ C ) )
                         => ( in @ A @ C ) ) ) ) )
            & ! [A: $i] :
                ( ( in @ A @ emptyset )
               => ! [B: $i] :
                    ( ( in @ B @ emptyset )
                   => ( ( A = B )
                      | ( in @ A @ B )
                      | ( in @ B @ A ) ) ) )
            & ! [A: $i] :
                ( ( in @ A @ emptyset )
               => ~ ( in @ A @ A ) )
            & ! [A: $i] :
                ( ( in @ A @ ( powerset @ emptyset ) )
               => ( ( A != emptyset )
                 => ? [B: $i] :
                      ( ( in @ B @ A )
                      & ! [C: $i] :
                          ( ( in @ C @ A )
                         => ( ( B = C )
                            | ( in @ B @ C ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(24,plain,
    ( sk1
    | sk3
    | ( in @ sk11 @ ( powerset @ emptyset ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(16,plain,
    ( ( in @ sk2 @ emptyset )
    | ~ sk1 ),
    inference(cnf,[status(esa)],[3]) ).

thf(25,plain,
    ! [B: $i,A: $i > $o] :
      ( ~ ( in @ B @ emptyset )
      | ( A @ B ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(58,plain,
    ! [B: $i,A: $i > $o] :
      ( ~ sk1
      | ( A @ B )
      | ( ( in @ sk2 @ emptyset )
       != ( in @ B @ emptyset ) ) ),
    inference(paramod_ordered,[status(thm)],[16,25]) ).

thf(59,plain,
    ! [A: $i > $o] :
      ( ~ sk1
      | ( A @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[58:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).

thf(11,plain,
    ( ~ ( subset @ sk2 @ emptyset )
    | ~ sk1 ),
    inference(cnf,[status(esa)],[3]) ).

thf(147,plain,
    ! [A: $i > $o] :
      ( ~ sk1
      | ( ( A @ sk2 )
       != ( subset @ sk2 @ emptyset ) ) ),
    inference(paramod_ordered,[status(thm)],[59,11]) ).

thf(162,plain,
    ~ sk1,
    inference(pre_uni,[status(thm)],[147:[bind(A,$thf( ^ [B: $i] : ( subset @ sk2 @ emptyset ) ))]]) ).

thf(183,plain,
    ( $false
    | sk3
    | ( in @ sk11 @ ( powerset @ emptyset ) ) ),
    inference(rewrite,[status(thm)],[24,162]) ).

thf(184,plain,
    ( sk3
    | ( in @ sk11 @ ( powerset @ emptyset ) ) ),
    inference(simp,[status(thm)],[183]) ).

thf(22,plain,
    ( sk1
    | sk4
    | ( in @ sk8 @ emptyset )
    | ( in @ sk10 @ emptyset )
    | ~ sk3 ),
    inference(cnf,[status(esa)],[3]) ).

thf(76,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ emptyset )
      | $false ),
    inference(prim_subst,[status(thm)],[25:[bind(A,$thf( ^ [C: $i] : $false ))]]) ).

thf(99,plain,
    ! [A: $i] :
      ~ ( in @ A @ emptyset ),
    inference(simp,[status(thm)],[76]) ).

thf(322,plain,
    ( $false
    | sk4
    | $false
    | $false
    | ~ sk3 ),
    inference(rewrite,[status(thm)],[22,162,99]) ).

thf(323,plain,
    ( sk4
    | ~ sk3 ),
    inference(simp,[status(thm)],[322]) ).

thf(6,plain,
    ( sk1
    | ( in @ sk7 @ emptyset )
    | ~ sk4
    | ~ sk3 ),
    inference(cnf,[status(esa)],[3]) ).

thf(226,plain,
    ( $false
    | ( in @ sk7 @ emptyset )
    | ~ sk4
    | ~ sk3 ),
    inference(rewrite,[status(thm)],[6,162]) ).

thf(227,plain,
    ( ( in @ sk7 @ emptyset )
    | ~ sk4
    | ~ sk3 ),
    inference(simp,[status(thm)],[226]) ).

thf(246,plain,
    ( $false
    | ~ sk4
    | ~ sk3 ),
    inference(rewrite,[status(thm)],[227,99]) ).

thf(247,plain,
    ( ~ sk4
    | ~ sk3 ),
    inference(simp,[status(thm)],[246]) ).

thf(324,plain,
    ( ~ sk3
    | ( sk4 != sk4 ) ),
    inference(paramod_ordered,[status(thm)],[323,247]) ).

thf(325,plain,
    ~ sk3,
    inference(pattern_uni,[status(thm)],[324:[]]) ).

thf(328,plain,
    ( $false
    | ( in @ sk11 @ ( powerset @ emptyset ) ) ),
    inference(rewrite,[status(thm)],[184,325]) ).

thf(329,plain,
    in @ sk11 @ ( powerset @ emptyset ),
    inference(simp,[status(thm)],[328]) ).

thf(13,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ B @ ( powerset @ A ) )
      | ( subset @ B @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(32,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ B @ ( powerset @ A ) )
      | ( subset @ B @ A ) ),
    inference(simp,[status(thm)],[13]) ).

thf(462,plain,
    ! [B: $i,A: $i] :
      ( ( subset @ B @ A )
      | ( ( in @ sk11 @ ( powerset @ emptyset ) )
       != ( in @ B @ ( powerset @ A ) ) ) ),
    inference(paramod_ordered,[status(thm)],[329,32]) ).

thf(463,plain,
    subset @ sk11 @ emptyset,
    inference(pattern_uni,[status(thm)],[462:[bind(A,$thf( emptyset )),bind(B,$thf( sk11 ))]]) ).

thf(23,plain,
    ! [A: $i] :
      ( ~ ( subset @ A @ emptyset )
      | ( A = emptyset ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(38,plain,
    ! [A: $i] :
      ( ( A = emptyset )
      | ~ ( subset @ A @ emptyset ) ),
    inference(lifteq,[status(thm)],[23]) ).

thf(39,plain,
    ! [A: $i] :
      ( ( A = emptyset )
      | ~ ( subset @ A @ emptyset ) ),
    inference(simp,[status(thm)],[38]) ).

thf(5,plain,
    ( sk1
    | sk3
    | ( sk11 != emptyset ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(30,plain,
    ( ( sk11 != emptyset )
    | sk1
    | sk3 ),
    inference(lifteq,[status(thm)],[5]) ).

thf(273,plain,
    ( ( sk11 != emptyset )
    | $false
    | sk3 ),
    inference(rewrite,[status(thm)],[30,162]) ).

thf(274,plain,
    ( ( sk11 != emptyset )
    | sk3 ),
    inference(simp,[status(thm)],[273]) ).

thf(275,plain,
    ! [A: $i] :
      ( ~ ( subset @ A @ emptyset )
      | sk3
      | ( A != sk11 ) ),
    inference(paramod_ordered,[status(thm)],[39,274]) ).

thf(276,plain,
    ( ~ ( subset @ sk11 @ emptyset )
    | sk3 ),
    inference(pattern_uni,[status(thm)],[275:[bind(A,$thf( sk11 ))]]) ).

thf(326,plain,
    ( ~ ( subset @ sk11 @ emptyset )
    | $false ),
    inference(rewrite,[status(thm)],[276,325]) ).

thf(327,plain,
    ~ ( subset @ sk11 @ emptyset ),
    inference(simp,[status(thm)],[326]) ).

thf(485,plain,
    $false,
    inference(rewrite,[status(thm)],[463,327]) ).

thf(486,plain,
    $false,
    inference(simp,[status(thm)],[485]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14  % Problem  : SEU820^2 : TPTP v8.2.0. Released v3.7.0.
% 0.13/0.17  % Command  : run_Leo-III %s %d
% 0.17/0.39  % Computer : n028.cluster.edu
% 0.17/0.39  % Model    : x86_64 x86_64
% 0.17/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.39  % Memory   : 8042.1875MB
% 0.17/0.39  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.39  % CPULimit : 300
% 0.17/0.39  % WCLimit  : 300
% 0.17/0.39  % DateTime : Sun May 19 17:12:39 EDT 2024
% 0.17/0.39  % CPUTime  : 
% 0.99/0.92  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.29/1.05  % [INFO] 	 Parsing done (127ms). 
% 1.29/1.06  % [INFO] 	 Running in sequential loop mode. 
% 1.76/1.35  % [INFO] 	 nitpick registered as external prover. 
% 1.76/1.36  % [INFO] 	 Scanning for conjecture ... 
% 1.88/1.45  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.16/1.49  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.16/1.49  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.16/1.49  % [INFO] 	 Type checking passed. 
% 2.24/1.50  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 6.27/2.63  % [INFO] 	 Killing All external provers ... 
% 6.27/2.64  % Time passed: 2070ms (effective reasoning time: 1571ms)
% 6.27/2.64  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 6.27/2.64  % Axioms used in derivation (0): 
% 6.27/2.64  % No. of inferences in proof: 44
% 6.27/2.64  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2070 ms resp. 1571 ms w/o parsing
% 6.27/2.68  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.27/2.68  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------