TSTP Solution File: SEU740^2 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU740^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n019.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 03:43:35 EDT 2024

% Result   : Theorem 4.29s 2.37s
% Output   : Refutation 4.32s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   26 (   8 unt;  10 typ;   2 def)
%            Number of atoms       :   54 (   4 equ;   0 cnn)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  171 (  10   ~;   5   |;   0   &; 131   @)
%                                         (   0 <=>;  25  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (  10 usr;   7 con; 0-2 aty)
%            Number of variables   :   42 (   0   ^  42   !;   0   ?;  42   :)

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

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

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

thf(binunionIL_type,type,
    binunionIL: $o ).

thf(binunionIL_def,definition,
    ( binunionIL
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( in @ C @ A )
         => ( in @ C @ ( binunion @ A @ B ) ) ) ) ) ).

thf(binintersect_type,type,
    binintersect: $i > $i > $i ).

thf(binintersectEL_type,type,
    binintersectEL: $o ).

thf(binintersectEL_def,definition,
    ( binintersectEL
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( in @ C @ ( binintersect @ A @ B ) )
         => ( in @ C @ A ) ) ) ) ).

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

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

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

thf(sk5_type,type,
    sk5: $i ).

thf(1,conjecture,
    ( binunionIL
   => ( binintersectEL
     => ! [A: $i,B: $i] :
          ( ( in @ B @ ( powerset @ A ) )
         => ! [C: $i] :
              ( ( in @ C @ ( powerset @ A ) )
             => ! [D: $i] :
                  ( ( in @ D @ ( powerset @ A ) )
                 => ! [E: $i] :
                      ( ( in @ E @ A )
                     => ( ( in @ E @ ( binintersect @ B @ C ) )
                       => ( in @ E @ ( binunion @ B @ D ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inIntersectImpInUnion) ).

thf(2,negated_conjecture,
    ~ ( binunionIL
     => ( binintersectEL
       => ! [A: $i,B: $i] :
            ( ( in @ B @ ( powerset @ A ) )
           => ! [C: $i] :
                ( ( in @ C @ ( powerset @ A ) )
               => ! [D: $i] :
                    ( ( in @ D @ ( powerset @ A ) )
                   => ! [E: $i] :
                        ( ( in @ E @ A )
                       => ( ( in @ E @ ( binintersect @ B @ C ) )
                         => ( in @ E @ ( binunion @ B @ D ) ) ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(4,plain,
    in @ sk5 @ ( binintersect @ sk2 @ sk3 ),
    inference(cnf,[status(esa)],[3]) ).

thf(8,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ ( binintersect @ A @ B ) )
      | ( in @ C @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(12,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ ( binintersect @ A @ B ) )
      | ( in @ C @ A ) ),
    inference(simp,[status(thm)],[8]) ).

thf(82,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ C @ A )
      | ( ( in @ sk5 @ ( binintersect @ sk2 @ sk3 ) )
       != ( in @ C @ ( binintersect @ A @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[4,12]) ).

thf(83,plain,
    in @ sk5 @ sk2,
    inference(pattern_uni,[status(thm)],[82:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 )),bind(C,$thf( sk5 ))]]) ).

thf(6,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ A )
      | ( in @ C @ ( binunion @ A @ B ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(7,plain,
    ~ ( in @ sk5 @ ( binunion @ sk2 @ sk4 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(33,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ A )
      | ( ( in @ C @ ( binunion @ A @ B ) )
       != ( in @ sk5 @ ( binunion @ sk2 @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[6,7]) ).

thf(34,plain,
    ~ ( in @ sk5 @ sk2 ),
    inference(pattern_uni,[status(thm)],[33:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 )),bind(C,$thf( sk5 ))]]) ).

thf(99,plain,
    $false,
    inference(rewrite,[status(thm)],[83,34]) ).

thf(100,plain,
    $false,
    inference(simp,[status(thm)],[99]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : SEU740^2 : TPTP v8.2.0. Released v3.7.0.
% 0.10/0.11  % Command  : run_Leo-III %s %d
% 0.11/0.31  % Computer : n019.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Sun May 19 15:33:54 EDT 2024
% 0.11/0.31  % CPUTime  : 
% 0.91/0.90  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.20/1.06  % [INFO] 	 Parsing done (159ms). 
% 1.20/1.07  % [INFO] 	 Running in sequential loop mode. 
% 1.72/1.41  % [INFO] 	 nitpick registered as external prover. 
% 1.72/1.42  % [INFO] 	 Scanning for conjecture ... 
% 1.96/1.52  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.04/1.55  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.04/1.55  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.04/1.56  % [INFO] 	 Type checking passed. 
% 2.04/1.56  % [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 ... 
% 4.29/2.37  % [INFO] 	 Killing All external provers ... 
% 4.29/2.37  % Time passed: 1919ms (effective reasoning time: 1295ms)
% 4.29/2.37  % 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)>
% 4.29/2.37  % Axioms used in derivation (0): 
% 4.29/2.37  % No. of inferences in proof: 14
% 4.29/2.37  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1919 ms resp. 1295 ms w/o parsing
% 4.32/2.41  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.32/2.41  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------