TSTP Solution File: SEU852^5 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU852^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n026.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 03:44:04 EDT 2024

% Result   : Theorem 3.63s 1.85s
% Output   : Refutation 3.63s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   26 (  15 unt;   5 typ;   0 def)
%            Number of atoms       :   66 (  10 equ;   0 cnn)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :  161 (  26   ~;   5   |;  23   &;  80   @)
%                                         (   0 <=>;  27  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   29 (   2   ^  27   !;   0   ?;  29   :)

% Comments : 
%------------------------------------------------------------------------------
thf(a_type,type,
    a: $tType ).

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

thf(sk2_type,type,
    sk2: a > $o ).

thf(sk3_type,type,
    sk3: a > $o ).

thf(sk6_type,type,
    sk6: a ).

thf(1,conjecture,
    ! [A: a > $o,B: a > $o,C: a > $o] :
      ( ( ! [D: a] :
            ( ( A @ D )
           => ( C @ D ) )
        & ! [D: a] :
            ( ( B @ D )
           => ( C @ D ) ) )
     => ( ( ! [D: a] :
              ( ( A @ D )
             => ( B @ D ) ) )
        = ( ! [D: a] :
              ( ( ( A @ D )
                & ( C @ D )
                & ~ ( B @ D ) )
             => ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGAZING_THM36_pme) ).

thf(2,negated_conjecture,
    ~ ! [A: a > $o,B: a > $o,C: a > $o] :
        ( ( ! [D: a] :
              ( ( A @ D )
             => ( C @ D ) )
          & ! [D: a] :
              ( ( B @ D )
             => ( C @ D ) ) )
       => ( ( ! [D: a] :
                ( ( A @ D )
               => ( B @ D ) ) )
          = ( ! [D: a] :
                ( ( ( A @ D )
                  & ( C @ D )
                  & ~ ( B @ D ) )
               => ( B @ D ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ! [A: a > $o,B: a > $o,C: a > $o] :
        ( ( ! [D: a] :
              ( ( A @ D )
             => ( C @ D ) )
          & ! [D: a] :
              ( ( B @ D )
             => ( C @ D ) ) )
       => ( ( ! [D: a] :
                ( ( A @ D )
               => ( B @ D ) ) )
          = ( ! [D: a] :
                ( ( ( A @ D )
                  & ( C @ D )
                  & ~ ( B @ D ) )
               => ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ! [A: a] :
          ( ( sk1 @ A )
         => ( sk2 @ A ) ) )
   != ( ! [A: a] :
          ( ( ( sk1 @ A )
            & ( sk3 @ A )
            & ~ ( sk2 @ A ) )
         => ( sk2 @ A ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(7,plain,
    ( ( ! [A: a] :
          ( ( ( sk1 @ A )
            & ( sk3 @ A )
            & ~ ( sk2 @ A ) )
         => ( sk2 @ A ) ) )
   != ( ! [A: a] :
          ( ( sk1 @ A )
         => ( sk2 @ A ) ) ) ),
    inference(lifteq,[status(thm)],[4]) ).

thf(9,plain,
    ( ( ^ [A: a] :
          ( ( ( sk1 @ A )
            & ( sk3 @ A )
            & ~ ( sk2 @ A ) )
         => ( sk2 @ A ) ) )
   != ( ^ [A: a] :
          ( ( sk1 @ A )
         => ( sk2 @ A ) ) ) ),
    inference(simp,[status(thm)],[7]) ).

thf(21,plain,
    ( ( ( ( sk1 @ sk6 )
        & ( sk3 @ sk6 )
        & ~ ( sk2 @ sk6 ) )
     => ( sk2 @ sk6 ) )
   != ( ( sk1 @ sk6 )
     => ( sk2 @ sk6 ) ) ),
    inference(func_ext,[status(esa)],[9]) ).

thf(41,plain,
    ( ~ ( ( ( sk1 @ sk6 )
          & ( sk3 @ sk6 )
          & ~ ( sk2 @ sk6 ) )
       => ( sk2 @ sk6 ) )
    | ~ ( ( sk1 @ sk6 )
       => ( sk2 @ sk6 ) ) ),
    inference(bool_ext,[status(thm)],[21]) ).

thf(58,plain,
    ( ( sk1 @ sk6 )
    | ( sk1 @ sk6 ) ),
    inference(cnf,[status(esa)],[41]) ).

thf(64,plain,
    sk1 @ sk6,
    inference(simp,[status(thm)],[58]) ).

thf(6,plain,
    ! [A: a] :
      ( ~ ( sk1 @ A )
      | ( sk3 @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(75,plain,
    ! [A: a] :
      ( ( sk3 @ A )
      | ( ( sk1 @ sk6 )
       != ( sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[64,6]) ).

thf(76,plain,
    sk3 @ sk6,
    inference(pattern_uni,[status(thm)],[75:[bind(A,$thf( sk6 ))]]) ).

thf(61,plain,
    ( ~ ( sk2 @ sk6 )
    | ~ ( sk2 @ sk6 ) ),
    inference(cnf,[status(esa)],[41]) ).

thf(63,plain,
    ~ ( sk2 @ sk6 ),
    inference(simp,[status(thm)],[61]) ).

thf(73,plain,
    ( ( ( ( sk1 @ sk6 )
        & ( sk3 @ sk6 )
        & ~ $false )
     => $false )
   != ( ( sk1 @ sk6 )
     => $false ) ),
    inference(rewrite,[status(thm)],[21,63]) ).

thf(74,plain,
    ( ( ( sk1 @ sk6 )
      & ( sk3 @ sk6 ) )
   != ( sk1 @ sk6 ) ),
    inference(simp,[status(thm)],[73]) ).

thf(78,plain,
    ~ ( $true
      & ( sk3 @ sk6 ) ),
    inference(rewrite,[status(thm)],[74,64]) ).

thf(79,plain,
    ~ ( sk3 @ sk6 ),
    inference(simp,[status(thm)],[78]) ).

thf(86,plain,
    $false,
    inference(rewrite,[status(thm)],[76,79]) ).

thf(87,plain,
    $false,
    inference(simp,[status(thm)],[86]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU852^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n026.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 17:09:39 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.98/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.16/0.97  % [INFO] 	 Parsing done (111ms). 
% 1.26/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.59/1.21  % [INFO] 	 nitpick registered as external prover. 
% 1.59/1.21  % [INFO] 	 Scanning for conjecture ... 
% 1.84/1.27  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.84/1.29  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.84/1.29  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.84/1.30  % [INFO] 	 Type checking passed. 
% 1.84/1.30  % [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 ... 
% 3.63/1.84  % [INFO] 	 Killing All external provers ... 
% 3.63/1.85  % Time passed: 1327ms (effective reasoning time: 861ms)
% 3.63/1.85  % 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)>
% 3.63/1.85  % Axioms used in derivation (0): 
% 3.63/1.85  % No. of inferences in proof: 21
% 3.63/1.85  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1327 ms resp. 861 ms w/o parsing
% 3.63/1.91  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.63/1.91  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------