TSTP Solution File: SEU818^2 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU818^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n018.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 3.44s 1.82s
% Output   : Refutation 3.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   23 (   8 unt;   9 typ;   3 def)
%            Number of atoms       :   88 (  10 equ;   0 cnn)
%            Maximal formula atoms :   50 (   6 avg)
%            Number of connectives :  211 (  10   ~;   9   |;  13   &; 135   @)
%                                         (   0 <=>;  44  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  11 usr;   8 con; 0-2 aty)
%            Number of variables   :   42 (   1   ^  39   !;   2   ?;  42   :)

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

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

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

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

thf(subsetI1_type,type,
    subsetI1: $o ).

thf(subsetI1_def,definition,
    ( subsetI1
    = ( ! [A: $i,B: $i] :
          ( ! [C: $i] :
              ( ( in @ C @ A )
             => ( in @ C @ B ) )
         => ( subset @ A @ B ) ) ) ) ).

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

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

thf(ordinalTransSet_type,type,
    ordinalTransSet: $o ).

thf(ordinalTransSet_def,definition,
    ( ordinalTransSet
    = ( ! [A: $i] :
          ( ( ordinal @ A )
         => ! [B: $i,C: $i] :
              ( ( in @ C @ A )
             => ( ( in @ B @ C )
               => ( in @ B @ A ) ) ) ) ) ) ).

thf(sk14_type,type,
    sk14: $i ).

thf(sk16_type,type,
    sk16: $i ).

thf(1,conjecture,
    ( subsetI1
   => ( ordinalTransSet
     => ! [A: $i] :
          ( ( ordinal @ A )
         => ! [B: $i] :
              ( ( in @ B @ A )
             => ( subset @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordinalTransSet1) ).

thf(2,negated_conjecture,
    ~ ( subsetI1
     => ( ordinalTransSet
       => ! [A: $i] :
            ( ( ordinal @ A )
           => ! [B: $i] :
                ( ( in @ B @ A )
               => ( subset @ B @ A ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(34,plain,
    in @ sk16 @ sk14,
    inference(cnf,[status(esa)],[3]) ).

thf(35,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ sk14 )
      | ( subset @ A @ sk14 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(48,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ sk14 )
      | ( subset @ A @ sk14 ) ),
    inference(simp,[status(thm)],[35]) ).

thf(73,plain,
    ! [A: $i] :
      ( ( subset @ A @ sk14 )
      | ( ( in @ sk16 @ sk14 )
       != ( in @ A @ sk14 ) ) ),
    inference(paramod_ordered,[status(thm)],[34,48]) ).

thf(74,plain,
    subset @ sk16 @ sk14,
    inference(pattern_uni,[status(thm)],[73:[bind(A,$thf( sk16 ))]]) ).

thf(4,plain,
    ~ ( subset @ sk16 @ sk14 ),
    inference(cnf,[status(esa)],[3]) ).

thf(77,plain,
    $false,
    inference(rewrite,[status(thm)],[74,4]) ).

thf(78,plain,
    $false,
    inference(simp,[status(thm)],[77]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU818^2 : TPTP v8.2.0. Released v3.7.0.
% 0.12/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n018.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Sun May 19 16:17:09 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.98/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.20/0.97  % [INFO] 	 Parsing done (116ms). 
% 1.20/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.67/1.20  % [INFO] 	 nitpick registered as external prover. 
% 1.67/1.20  % [INFO] 	 Scanning for conjecture ... 
% 1.81/1.29  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.81/1.30  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.81/1.30  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.81/1.31  % [INFO] 	 Type checking passed. 
% 1.81/1.31  % [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 ... 
% 3.43/1.81  % [INFO] 	 Killing All external provers ... 
% 3.44/1.82  % Time passed: 1295ms (effective reasoning time: 829ms)
% 3.44/1.82  % 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)>
% 3.44/1.82  % Axioms used in derivation (0): 
% 3.44/1.82  % No. of inferences in proof: 11
% 3.44/1.82  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1295 ms resp. 829 ms w/o parsing
% 3.44/1.85  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.44/1.85  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------