TSTP Solution File: SEU623^2 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU623^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n004.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 03:43:02 EDT 2024

% Result   : Theorem 4.05s 1.86s
% Output   : Refutation 4.05s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   38 (  13 unt;  13 typ;   4 def)
%            Number of atoms       :   81 (   7 equ;   0 cnn)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  251 (  17   ~;  10   |;   0   &; 192   @)
%                                         (   0 <=>;  32  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  13 usr;  10 con; 0-2 aty)
%            Number of variables   :   62 (   0   ^  62   !;   0   ?;  62   :)

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

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

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

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

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

thf(subsetE_type,type,
    subsetE: $o ).

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

thf(powersetsubset_type,type,
    powersetsubset: $o ).

thf(powersetsubset_def,definition,
    ( powersetsubset
    = ( ! [A: $i,B: $i] :
          ( ( subset @ A @ B )
         => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).

thf(binunion_type,type,
    binunion: $i > $i > $i ).

thf(binunionLsub_type,type,
    binunionLsub: $o ).

thf(binunionLsub_def,definition,
    ( binunionLsub
    = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).

thf(singletoninpowerset_type,type,
    singletoninpowerset: $o ).

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

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

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

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

thf(1,conjecture,
    ( subsetE
   => ( powersetsubset
     => ( binunionLsub
       => ( singletoninpowerset
         => ! [A: $i,B: $i,C: $i] :
              ( ( in @ C @ A )
             => ( in @ ( setadjoin @ C @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletoninpowunion) ).

thf(2,negated_conjecture,
    ~ ( subsetE
     => ( powersetsubset
       => ( binunionLsub
         => ( singletoninpowerset
           => ! [A: $i,B: $i,C: $i] :
                ( ( in @ C @ A )
               => ( in @ ( setadjoin @ C @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(4,plain,
    ~ ( ! [A: $i,B: $i] :
          ( ( subset @ A @ B )
         => ! [C: $i] :
              ( ( in @ C @ A )
             => ( in @ C @ B ) ) )
     => ( ! [A: $i,B: $i] :
            ( ( subset @ A @ B )
           => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) )
       => ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) )
         => ( ! [A: $i,B: $i] :
                ( ( in @ B @ A )
               => ( in @ ( setadjoin @ B @ emptyset ) @ ( powerset @ A ) ) )
           => ! [A: $i,B: $i,C: $i] :
                ( ( in @ C @ A )
               => ( in @ ( setadjoin @ C @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ),
    inference(miniscope,[status(thm)],[3]) ).

thf(7,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ B @ A )
      | ( in @ ( setadjoin @ B @ emptyset ) @ ( powerset @ A ) ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(12,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ B @ A )
      | ( in @ ( setadjoin @ B @ emptyset ) @ ( powerset @ A ) ) ),
    inference(simp,[status(thm)],[7]) ).

thf(10,plain,
    ~ ( in @ ( setadjoin @ sk3 @ emptyset ) @ ( powerset @ ( binunion @ sk1 @ sk2 ) ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(64,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ B @ A )
      | ( ( in @ ( setadjoin @ B @ emptyset ) @ ( powerset @ A ) )
       != ( in @ ( setadjoin @ sk3 @ emptyset ) @ ( powerset @ ( binunion @ sk1 @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[12,10]) ).

thf(65,plain,
    ~ ( in @ sk3 @ ( binunion @ sk1 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[64:[bind(A,$thf( binunion @ sk1 @ sk2 )),bind(B,$thf( sk3 ))]]) ).

thf(9,plain,
    ! [B: $i,A: $i] : ( subset @ A @ ( binunion @ A @ B ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(11,plain,
    ! [B: $i,A: $i] : ( subset @ A @ ( binunion @ A @ B ) ),
    inference(simp,[status(thm)],[9]) ).

thf(5,plain,
    in @ sk3 @ sk1,
    inference(cnf,[status(esa)],[4]) ).

thf(6,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( subset @ A @ B )
      | ~ ( in @ C @ A )
      | ( in @ C @ B ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(16,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( subset @ A @ B )
      | ( in @ C @ B )
      | ( ( in @ sk3 @ sk1 )
       != ( in @ C @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[5,6]) ).

thf(17,plain,
    ! [A: $i] :
      ( ~ ( subset @ sk1 @ A )
      | ( in @ sk3 @ A ) ),
    inference(pattern_uni,[status(thm)],[16:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( sk3 ))]]) ).

thf(23,plain,
    ! [A: $i] :
      ( ~ ( subset @ sk1 @ A )
      | ( in @ sk3 @ A ) ),
    inference(simp,[status(thm)],[17]) ).

thf(48,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ sk3 @ C )
      | ( ( subset @ A @ ( binunion @ A @ B ) )
       != ( subset @ sk1 @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[11,23]) ).

thf(49,plain,
    ! [A: $i] : ( in @ sk3 @ ( binunion @ sk1 @ A ) ),
    inference(pattern_uni,[status(thm)],[48:[bind(A,$thf( sk1 )),bind(B,$thf( E )),bind(C,$thf( binunion @ sk1 @ E ))]]) ).

thf(50,plain,
    ! [A: $i] : ( in @ sk3 @ ( binunion @ sk1 @ A ) ),
    inference(simp,[status(thm)],[49]) ).

thf(82,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[65,50]) ).

thf(83,plain,
    $false,
    inference(simp,[status(thm)],[82]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU623^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n004.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Sun May 19 16:31:54 EDT 2024
% 0.15/0.37  % CPUTime  : 
% 0.95/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.19/0.96  % [INFO] 	 Parsing done (101ms). 
% 1.19/0.96  % [INFO] 	 Running in sequential loop mode. 
% 1.54/1.16  % [INFO] 	 nitpick registered as external prover. 
% 1.54/1.16  % [INFO] 	 Scanning for conjecture ... 
% 1.65/1.23  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.88/1.25  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.88/1.25  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.88/1.25  % [INFO] 	 Type checking passed. 
% 1.88/1.25  % [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 ... 
% 4.05/1.86  % [INFO] 	 Killing All external provers ... 
% 4.05/1.86  % Time passed: 1336ms (effective reasoning time: 890ms)
% 4.05/1.86  % 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)>
% 4.05/1.86  % Axioms used in derivation (0): 
% 4.05/1.86  % No. of inferences in proof: 21
% 4.05/1.86  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1336 ms resp. 890 ms w/o parsing
% 4.05/1.90  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.05/1.90  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------