TSTP Solution File: SYO016^1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SYO016^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n024.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 08:55:26 EDT 2024

% Result   : Theorem 6.96s 2.18s
% Output   : Refutation 6.96s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   24 (   7 unt;   4 typ;   1 def)
%            Number of atoms       :  112 (   7 equ;   0 cnn)
%            Maximal formula atoms :    9 (   5 avg)
%            Number of connectives :  123 (  15   ~;   3   |;   0   &;  94   @)
%                                         (   0 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   19 (  19   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   16 (   2   ^  14   !;   0   ?;  16   :)

% Comments : 
%------------------------------------------------------------------------------
thf(leibeq_type,type,
    leibeq: $o > $o > $o ).

thf(leibeq_def,definition,
    ( leibeq
    = ( ^ [A: $o,B: $o] :
        ! [C: $o > $o] :
          ( ( C @ A )
         => ( C @ B ) ) ) ) ).

thf(h_type,type,
    h: $o > $o ).

thf(sk1_type,type,
    sk1: $o > $o ).

thf(sk22_type,type,
    sk22: $o > $o ).

thf(1,conjecture,
    leibeq @ ( h @ ( leibeq @ ( h @ $true ) @ ( h @ $false ) ) ) @ ( h @ $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).

thf(2,negated_conjecture,
    ~ ( leibeq @ ( h @ ( leibeq @ ( h @ $true ) @ ( h @ $false ) ) ) @ ( h @ $false ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ! [A: $o > $o] :
        ( ( A
          @ ( h
            @ ! [B: $o > $o] :
                ( ( B @ ( h @ $true ) )
               => ( B @ ( h @ $false ) ) ) ) )
       => ( A @ ( h @ $false ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(5,plain,
    ( sk1
    @ ( h
      @ ! [A: $o > $o] :
          ( ( A @ ( h @ $true ) )
         => ( A @ ( h @ $false ) ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(4,plain,
    ~ ( sk1 @ ( h @ $false ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(6,plain,
    ( ( sk1
      @ ( h
        @ ! [A: $o > $o] :
            ( ( A @ ( h @ $true ) )
           => ( A @ ( h @ $false ) ) ) ) )
   != ( sk1 @ ( h @ $false ) ) ),
    inference(paramod_ordered,[status(thm)],[5,4]) ).

thf(7,plain,
    ( ( h
      @ ! [A: $o > $o] :
          ( ( A @ ( h @ $true ) )
         => ( A @ ( h @ $false ) ) ) )
   != ( h @ $false ) ),
    inference(simp,[status(thm)],[6]) ).

thf(8,plain,
    ! [A: $o > $o] :
      ( ( A @ ( h @ $true ) )
     => ( A @ ( h @ $false ) ) ),
    inference(simp,[status(thm)],[7]) ).

thf(11,plain,
    ! [A: $o > $o] :
      ( ~ ( A @ ( h @ $true ) )
      | ( A @ ( h @ $false ) ) ),
    inference(cnf,[status(esa)],[8]) ).

thf(263,plain,
    ! [A: $o > $o] :
      ( ~ ( A @ ( h @ $true ) )
      | ( ( A @ ( h @ $false ) )
       != ( sk1 @ ( h @ $false ) ) ) ),
    inference(paramod_ordered,[status(thm)],[11,4]) ).

thf(400,plain,
    ~ ( sk1 @ ( h @ $true ) ),
    inference(pre_uni,[status(thm)],[263:[bind(A,$thf( sk1 ))]]) ).

thf(470,plain,
    ( ( sk1
      @ ( h
        @ ! [A: $o > $o] :
            ( ( A @ ( h @ $true ) )
           => ( A @ ( h @ $false ) ) ) ) )
   != ( sk1 @ ( h @ $true ) ) ),
    inference(paramod_ordered,[status(thm)],[5,400]) ).

thf(482,plain,
    ( ( h
      @ ! [A: $o > $o] :
          ( ( A @ ( h @ $true ) )
         => ( A @ ( h @ $false ) ) ) )
   != ( h @ $true ) ),
    inference(simp,[status(thm)],[470]) ).

thf(501,plain,
    ! [A: $o > $o] :
      ( ~ ( A @ ( h @ $true ) )
      | ( ( ! [B: $o > $o] :
              ( ( B @ ( h @ $true ) )
             => ( B @ ( h @ $false ) ) ) )
       != ( A @ ( h @ $false ) ) ) ),
    inference(paramod_ordered,[status(thm)],[11,482]) ).

thf(533,plain,
    ~ ! [A: $o > $o] :
        ( ( A @ ( h @ $true ) )
       => ( A @ ( h @ $true ) ) ),
    inference(pre_uni,[status(thm)],[501:[bind(A,$thf( ^ [B: $o] : ! [C: $o > $o] : ( ( C @ ( h @ $true ) ) => ( C @ B ) ) ))]]) ).

thf(554,plain,
    sk22 @ ( h @ $true ),
    inference(cnf,[status(esa)],[533]) ).

thf(553,plain,
    ~ ( sk22 @ ( h @ $true ) ),
    inference(cnf,[status(esa)],[533]) ).

thf(575,plain,
    $false,
    inference(rewrite,[status(thm)],[554,553]) ).

thf(576,plain,
    $false,
    inference(simp,[status(thm)],[575]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SYO016^1 : TPTP v8.2.0. Released v3.7.0.
% 0.13/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n024.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 : Mon May 20 09:51:54 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.87/0.80  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.15/0.89  % [INFO] 	 Parsing done (91ms). 
% 1.15/0.90  % [INFO] 	 Running in sequential loop mode. 
% 1.54/1.10  % [INFO] 	 eprover registered as external prover. 
% 1.54/1.10  % [INFO] 	 cvc4 registered as external prover. 
% 1.54/1.10  % [INFO] 	 Scanning for conjecture ... 
% 1.54/1.15  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.76/1.17  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.76/1.17  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.76/1.17  % [INFO] 	 Type checking passed. 
% 1.76/1.17  % [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 ... 
% 6.31/2.18  % [INFO] 	 Killing All external provers ... 
% 6.96/2.18  % Time passed: 1649ms (effective reasoning time: 1275ms)
% 6.96/2.18  % 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)>
% 6.96/2.18  % Axioms used in derivation (0): 
% 6.96/2.18  % No. of inferences in proof: 19
% 6.96/2.18  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1649 ms resp. 1275 ms w/o parsing
% 6.96/2.20  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.96/2.20  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------