TSTP Solution File: SEU519_8 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SEU519_8 : TPTP v8.1.2. Released v8.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n020.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 : Fri May 19 11:59:30 EDT 2023

% Result   : Theorem 3.05s 1.80s
% Output   : Refutation 3.28s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   30 (  16 unt;   7 typ;   0 def)
%            Number of atoms       :   55 (   8 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :  110 (   9   ~;   4   |;   0   &;  79   @)
%                                         (   0 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :   35 (   0   ^;  35   !;   0   ?;  35   :)

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

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

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

thf(emptysetE_type,type,
    emptysetE: $o ).

thf(powersetI_type,type,
    powersetI: $o ).

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

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

thf(1,conjecture,
    ( emptysetE
   => ( powersetI
     => ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset) ).

thf(2,negated_conjecture,
    ~ ( emptysetE
     => ( powersetI
       => ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(5,plain,
    ~ ( emptysetE
     => ( powersetI
       => ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(6,plain,
    ~ ( in @ emptyset @ ( powerset @ sk1 ) ),
    inference(cnf,[status(esa)],[5]) ).

thf(3,axiom,
    ( powersetI
    = ( ! [A: $i,B: $i] :
          ( ! [C: $i] :
              ( ( in @ C @ B )
             => ( in @ C @ A ) )
         => ( in @ B @ ( powerset @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI) ).

thf(9,plain,
    ( powersetI
    = ( ! [A: $i,B: $i] :
          ( ! [C: $i] :
              ( ( in @ C @ B )
             => ( in @ C @ A ) )
         => ( in @ B @ ( powerset @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(10,plain,
    ( powersetI
    = ( ! [A: $i,B: $i] :
          ( ! [C: $i] :
              ( ( in @ C @ B )
             => ( in @ C @ A ) )
         => ( in @ B @ ( powerset @ A ) ) ) ) ),
    inference(lifteq,[status(thm)],[9]) ).

thf(7,plain,
    powersetI,
    inference(cnf,[status(esa)],[5]) ).

thf(38,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( in @ C @ B )
         => ( in @ C @ A ) )
     => ( in @ B @ ( powerset @ A ) ) ),
    inference(rewrite,[status(thm)],[10,7]) ).

thf(39,plain,
    ! [B: $i,A: $i] :
      ( ( in @ ( sk2 @ B @ A ) @ B )
      | ( in @ B @ ( powerset @ A ) ) ),
    inference(cnf,[status(esa)],[38]) ).

thf(4,axiom,
    ( emptysetE
    = ( ! [A: $i] :
          ( ( in @ A @ emptyset )
         => ! [B: $o] : B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).

thf(11,plain,
    ( emptysetE
    = ( ! [A: $i] :
          ( ( in @ A @ emptyset )
         => ! [B: $o] : B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(12,plain,
    ( emptysetE
    = ( ! [A: $i] :
          ( ( in @ A @ emptyset )
         => ! [B: $o] : B ) ) ),
    inference(lifteq,[status(thm)],[11]) ).

thf(8,plain,
    emptysetE,
    inference(cnf,[status(esa)],[5]) ).

thf(13,plain,
    ! [A: $i] :
      ( ( in @ A @ emptyset )
     => ! [B: $o] : B ),
    inference(rewrite,[status(thm)],[12,8]) ).

thf(14,plain,
    ! [B: $o,A: $i] :
      ( ~ ( in @ A @ emptyset )
      | B ),
    inference(cnf,[status(esa)],[13]) ).

thf(15,plain,
    ! [B: $o,A: $i] :
      ( ~ ( in @ A @ emptyset )
      | ( B
       != ( in @ emptyset @ ( powerset @ sk1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[14,6]) ).

thf(16,plain,
    ! [A: $i] :
      ~ ( in @ A @ emptyset ),
    inference(pattern_uni,[status(thm)],[15:[bind(A,$thf( A )),bind(B,$thf( in @ emptyset @ ( powerset @ sk1 ) ))]]) ).

thf(50,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ B @ ( powerset @ A ) )
      | ( ( in @ ( sk2 @ B @ A ) @ B )
       != ( in @ C @ emptyset ) ) ),
    inference(paramod_ordered,[status(thm)],[39,16]) ).

thf(51,plain,
    ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ),
    inference(pattern_uni,[status(thm)],[50:[bind(A,$thf( E )),bind(B,$thf( emptyset )),bind(C,$thf( sk2 @ emptyset @ E ))]]) ).

thf(58,plain,
    ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ),
    inference(simp,[status(thm)],[51]) ).

thf(62,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[6,58]) ).

thf(63,plain,
    $false,
    inference(simp,[status(thm)],[62]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SEU519_8 : TPTP v8.1.2. Released v8.0.0.
% 0.10/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n020.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 : Thu May 18 13:34:18 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.99/0.88  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.31/1.00  % [INFO] 	 Parsing done (121ms). 
% 1.31/1.01  % [INFO] 	 Running in sequential loop mode. 
% 1.66/1.23  % [INFO] 	 eprover registered as external prover. 
% 1.66/1.23  % [INFO] 	 cvc4 registered as external prover. 
% 1.66/1.23  % [INFO] 	 Scanning for conjecture ... 
% 1.66/1.27  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 1.66/1.28  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 1.91/1.30  % [INFO] 	 Found a conjecture and 2 axioms. Running axiom selection ... 
% 1.91/1.32  % [INFO] 	 Axiom selection finished. Selected 2 axioms (removed 0 axioms). 
% 1.91/1.32  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 1.91/1.32  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 1.91/1.32  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 1.91/1.33  % [INFO] 	 Type checking passed. 
% 1.91/1.33  % [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 ... 
% 3.05/1.79  % [INFO] 	 Killing All external provers ... 
% 3.05/1.79  % Time passed: 1277ms (effective reasoning time: 776ms)
% 3.05/1.79  % 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)>
% 3.05/1.80  % Axioms used in derivation (2): powersetI, emptysetE
% 3.05/1.80  % No. of inferences in proof: 23
% 3.05/1.80  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1277 ms resp. 776 ms w/o parsing
% 3.28/1.82  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.28/1.82  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------