TSTP Solution File: SEU819^2 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU819^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n007.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 03:40:10 EDT 2024

% Result   : Theorem 3.07s 1.91s
% Output   : Refutation 3.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   15 (   4 unt;   8 typ;   3 def)
%            Number of atoms       :   51 (   6 equ;   0 cnn)
%            Maximal formula atoms :   29 (   7 avg)
%            Number of connectives :  120 (   4   ~;   3   |;   7   &;  78   @)
%                                         (   0 <=>;  28  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   9 usr;   4 con; 0-2 aty)
%            Number of variables   :   26 (   2   ^  23   !;   1   ?;  26   :)

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

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

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

thf(setunion_type,type,
    setunion: $i > $i ).

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

thf(transitiveset_type,type,
    transitiveset: $i > $o ).

thf(transitiveset_def,definition,
    ( transitiveset
    = ( ^ [A: $i] :
        ! [B: $i] :
          ( ( in @ B @ A )
         => ( subset @ B @ A ) ) ) ) ).

thf(setunionTransitive_type,type,
    setunionTransitive: $o ).

thf(setunionTransitive_def,definition,
    ( setunionTransitive
    = ( ! [A: $i] :
          ( ! [B: $i] :
              ( ( in @ B @ A )
             => ( transitiveset @ B ) )
         => ( transitiveset @ ( setunion @ A ) ) ) ) ) ).

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

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

thf(1,conjecture,
    ( setunionTransitive
   => ! [A: $i] :
        ( ! [B: $i] :
            ( ( in @ B @ A )
           => ( ordinal @ B ) )
       => ( transitiveset @ ( setunion @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionOrdinalLem1) ).

thf(2,negated_conjecture,
    ~ ( setunionTransitive
     => ! [A: $i] :
          ( ! [B: $i] :
              ( ( in @ B @ A )
             => ( ordinal @ B ) )
         => ( transitiveset @ ( setunion @ A ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(24,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12  % Problem  : SEU819^2 : TPTP v8.2.0. Released v3.7.0.
% 0.09/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.36  % Computer : n007.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Sun May 19 16:23:54 EDT 2024
% 0.14/0.36  % CPUTime  : 
% 0.96/0.90  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.23/1.04  % [INFO] 	 Parsing done (139ms). 
% 1.23/1.05  % [INFO] 	 Running in sequential loop mode. 
% 1.70/1.29  % [INFO] 	 eprover registered as external prover. 
% 1.70/1.29  % [INFO] 	 cvc4 registered as external prover. 
% 1.70/1.30  % [INFO] 	 Scanning for conjecture ... 
% 2.05/1.40  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.05/1.43  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.05/1.43  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.05/1.43  % [INFO] 	 Type checking passed. 
% 2.05/1.43  % [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 ... 
% 3.07/1.90  % External prover 'e' found a proof!
% 3.07/1.90  % [INFO] 	 Killing All external provers ... 
% 3.07/1.90  % Time passed: 1377ms (effective reasoning time: 851ms)
% 3.07/1.90  % 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)>
% 3.07/1.90  % Axioms used in derivation (0): 
% 3.07/1.90  % No. of inferences in proof: 4
% 3.07/1.91  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1377 ms resp. 851 ms w/o parsing
% 3.38/1.95  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.38/1.95  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------