TSTP Solution File: SEU706^2 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU706^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n005.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 03:43:25 EDT 2024

% Result   : Theorem 4.68s 2.21s
% Output   : Refutation 4.68s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   41 (  20 unt;  13 typ;   6 def)
%            Number of atoms       :   85 (  47 equ;   0 cnn)
%            Maximal formula atoms :   15 (   3 avg)
%            Number of connectives :  154 (  15   ~;   6   |;   2   &;  98   @)
%                                         (   0 <=>;  33  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  13 usr;  10 con; 0-2 aty)
%            Number of variables   :   46 (   1   ^  43   !;   2   ?;  46   :)

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

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

thf(setadjoin_type,type,
    setadjoin: $i > $i > $i ).

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

thf(uniqinunit_type,type,
    uniqinunit: $o ).

thf(uniqinunit_def,definition,
    ( uniqinunit
    = ( ! [A: $i,B: $i] :
          ( ( in @ A @ ( setadjoin @ B @ emptyset ) )
         => ( A = B ) ) ) ) ).

thf(in__Cong_type,type,
    in__Cong: $o ).

thf(in__Cong_def,definition,
    ( in__Cong
    = ( ! [A: $i,B: $i] :
          ( ( A = B )
         => ! [C: $i,D: $i] :
              ( ( C = D )
             => ( ( in @ C @ A )
                = ( in @ D @ B ) ) ) ) ) ) ).

thf(setadjoin__Cong_type,type,
    setadjoin__Cong: $o ).

thf(setadjoin__Cong_def,definition,
    ( setadjoin__Cong
    = ( ! [A: $i,B: $i] :
          ( ( A = B )
         => ! [C: $i,D: $i] :
              ( ( C = D )
             => ( ( setadjoin @ A @ C )
                = ( setadjoin @ B @ D ) ) ) ) ) ) ).

thf(setunion__Cong_type,type,
    setunion__Cong: $o ).

thf(setunion__Cong_def,definition,
    ( setunion__Cong
    = ( ! [A: $i,B: $i] :
          ( ( A = B )
         => ( ( setunion @ A )
            = ( setunion @ B ) ) ) ) ) ).

thf(setunionsingleton_type,type,
    setunionsingleton: $o ).

thf(setunionsingleton_def,definition,
    ( setunionsingleton
    = ( ! [A: $i] :
          ( ( setunion @ ( setadjoin @ A @ emptyset ) )
          = A ) ) ) ).

thf(singleton_type,type,
    singleton: $i > $o ).

thf(singleton_def,definition,
    ( singleton
    = ( ^ [A: $i] :
        ? [B: $i] :
          ( ( in @ B @ A )
          & ( A
            = ( setadjoin @ B @ emptyset ) ) ) ) ) ).

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

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

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

thf(1,conjecture,
    ( uniqinunit
   => ( in__Cong
     => ( setadjoin__Cong
       => ( setunion__Cong
         => ( setunionsingleton
           => ! [A: $i] :
                ( ( singleton @ A )
               => ! [B: $i] :
                    ( ( in @ B @ A )
                   => ( ( setunion @ A )
                      = B ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theeq) ).

thf(2,negated_conjecture,
    ~ ( uniqinunit
     => ( in__Cong
       => ( setadjoin__Cong
         => ( setunion__Cong
           => ( setunionsingleton
             => ! [A: $i] :
                  ( ( singleton @ A )
                 => ! [B: $i] :
                      ( ( in @ B @ A )
                     => ( ( setunion @ A )
                        = B ) ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(5,plain,
    in @ sk3 @ sk1,
    inference(cnf,[status(esa)],[3]) ).

thf(10,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(13,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( in @ A @ ( setadjoin @ B @ emptyset ) ) ),
    inference(lifteq,[status(thm)],[10]) ).

thf(8,plain,
    ( ( setunion @ sk1 )
   != sk3 ),
    inference(cnf,[status(esa)],[3]) ).

thf(23,plain,
    ( ( setunion @ sk1 )
   != sk3 ),
    inference(lifteq,[status(thm)],[8]) ).

thf(6,plain,
    ( sk1
    = ( setadjoin @ sk2 @ emptyset ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(14,plain,
    ( ( setadjoin @ sk2 @ emptyset )
    = sk1 ),
    inference(lifteq,[status(thm)],[6]) ).

thf(11,plain,
    ! [A: $i] :
      ( ( setunion @ ( setadjoin @ A @ emptyset ) )
      = A ),
    inference(cnf,[status(esa)],[3]) ).

thf(21,plain,
    ! [A: $i] :
      ( ( setunion @ ( setadjoin @ A @ emptyset ) )
      = A ),
    inference(lifteq,[status(thm)],[11]) ).

thf(22,plain,
    ! [A: $i] :
      ( ( setunion @ ( setadjoin @ A @ emptyset ) )
      = A ),
    inference(simp,[status(thm)],[21]) ).

thf(122,plain,
    ! [A: $i] :
      ( ( ( setunion @ sk1 )
        = A )
      | ( ( setadjoin @ sk2 @ emptyset )
       != ( setadjoin @ A @ emptyset ) ) ),
    inference(paramod_ordered,[status(thm)],[14,22]) ).

thf(123,plain,
    ( ( setunion @ sk1 )
    = sk2 ),
    inference(pattern_uni,[status(thm)],[122:[bind(A,$thf( sk2 ))]]) ).

thf(148,plain,
    sk3 != sk2,
    inference(rewrite,[status(thm)],[23,123]) ).

thf(163,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( B != sk2 )
      | ( A != sk3 ) ),
    inference(paramod_ordered,[status(thm)],[13,148]) ).

thf(164,plain,
    ! [A: $i] :
      ( ~ ( in @ sk3 @ ( setadjoin @ A @ emptyset ) )
      | ( A != sk2 ) ),
    inference(pattern_uni,[status(thm)],[163:[bind(A,$thf( sk3 ))]]) ).

thf(167,plain,
    ~ ( in @ sk3 @ ( setadjoin @ sk2 @ emptyset ) ),
    inference(simp,[status(thm)],[164]) ).

thf(241,plain,
    ~ ( in @ sk3 @ sk1 ),
    inference(rewrite,[status(thm)],[167,14]) ).

thf(242,plain,
    $false,
    inference(rewrite,[status(thm)],[5,241]) ).

thf(243,plain,
    $false,
    inference(simp,[status(thm)],[242]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SEU706^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n005.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Sun May 19 17:37:09 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 1.07/0.95  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.37/1.08  % [INFO] 	 Parsing done (125ms). 
% 1.42/1.09  % [INFO] 	 Running in sequential loop mode. 
% 1.74/1.33  % [INFO] 	 nitpick registered as external prover. 
% 1.88/1.34  % [INFO] 	 Scanning for conjecture ... 
% 2.11/1.42  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.11/1.44  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.11/1.44  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.11/1.45  % [INFO] 	 Type checking passed. 
% 2.11/1.45  % [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 ... 
% 4.68/2.21  % [INFO] 	 Killing All external provers ... 
% 4.68/2.21  % Time passed: 1641ms (effective reasoning time: 1118ms)
% 4.68/2.21  % 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)>
% 4.68/2.21  % Axioms used in derivation (0): 
% 4.68/2.21  % No. of inferences in proof: 22
% 4.68/2.21  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1641 ms resp. 1118 ms w/o parsing
% 4.68/2.24  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.68/2.24  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------