TSTP Solution File: SYO304^5 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SYO304^5 : TPTP v8.2.0. Released v4.0.0.
% 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 08:59:51 EDT 2024

% Result   : Theorem 3.71s 1.96s
% Output   : Refutation 3.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   28 (  15 unt;   5 typ;   0 def)
%            Number of atoms       :   36 (  27 equ;   6 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   95 (  22   ~;  13   |;   0   &;  46   @)
%                                         (   0 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   26 (  26   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   4 con; 0-2 aty)
%            Number of variables   :   28 (  12   ^  16   !;   0   ?;  28   :)

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

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

thf(sk2_type,type,
    sk2: a ).

thf(sk3_type,type,
    sk3: a ).

thf(sk4_type,type,
    sk4: a > $o ).

thf(1,conjecture,
    ! [A: ( a > a > $o ) > $o] :
      ( ( A
        @ ^ [B: a,C: a] :
          ! [D: a > $o] :
            ( ( D @ B )
           => ( D @ C ) ) )
     => ( A @ ( (=) @ a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cE2_eq__pme) ).

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

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

thf(5,plain,
    ( sk1
    @ ^ [A: a,B: a] :
      ! [C: a > $o] :
        ( ( C @ A )
       => ( C @ B ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(4,plain,
    ~ ( sk1 @ ( (=) @ a ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(6,plain,
    ( ( sk1
      @ ^ [A: a,B: a] :
        ! [C: a > $o] :
          ( ( C @ A )
         => ( C @ B ) ) )
   != ( sk1 @ ( (=) @ a ) ) ),
    inference(paramod_ordered,[status(thm)],[5,4]) ).

thf(7,plain,
    ( ( ^ [A: a,B: a] :
        ! [C: a > $o] :
          ( ( C @ A )
         => ( C @ B ) ) )
   != ( (=) @ a ) ),
    inference(simp,[status(thm)],[6]) ).

thf(8,plain,
    ( ( ! [A: a > $o] :
          ( ( A @ sk2 )
         => ( A @ sk3 ) ) )
   != ( sk2 = sk3 ) ),
    inference(func_ext,[status(esa)],[7]) ).

thf(10,plain,
    ( ! [A: a > $o] :
        ( ( A @ sk2 )
       => ( A @ sk3 ) )
    | ( sk2 = sk3 ) ),
    inference(bool_ext,[status(thm)],[8]) ).

thf(12,plain,
    ( ( sk3 = sk2 )
    | ! [A: a > $o] :
        ( ( A @ sk2 )
       => ( A @ sk3 ) ) ),
    inference(lifteq,[status(thm)],[10]) ).

thf(15,plain,
    ! [A: a > $o] :
      ( ~ ( A @ sk2 )
      | ( A @ sk3 )
      | ( sk3 = sk2 ) ),
    inference(cnf,[status(esa)],[12]) ).

thf(9,plain,
    ( ~ ! [A: a > $o] :
          ( ( A @ sk2 )
         => ( A @ sk3 ) )
    | ( sk2 != sk3 ) ),
    inference(bool_ext,[status(thm)],[8]) ).

thf(11,plain,
    ( ( sk3 != sk2 )
    | ~ ! [A: a > $o] :
          ( ( A @ sk2 )
         => ( A @ sk3 ) ) ),
    inference(lifteq,[status(thm)],[9]) ).

thf(14,plain,
    ( ( sk4 @ sk2 )
    | ( sk3 != sk2 ) ),
    inference(cnf,[status(esa)],[11]) ).

thf(13,plain,
    ( ~ ( sk4 @ sk3 )
    | ( sk3 != sk2 ) ),
    inference(cnf,[status(esa)],[11]) ).

thf(16,plain,
    ( ( sk3 != sk2 )
    | ( ( sk4 @ sk3 )
     != ( sk4 @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[14,13]) ).

thf(17,plain,
    ( ( sk3 != sk2 )
    | ( sk3 != sk2 ) ),
    inference(simp,[status(thm)],[16]) ).

thf(18,plain,
    sk3 != sk2,
    inference(simp,[status(thm)],[17]) ).

thf(92,plain,
    ! [A: a > $o] :
      ( ~ ( A @ sk2 )
      | ( A @ sk3 ) ),
    inference(simplifyReflect,[status(thm)],[15,18]) ).

thf(93,plain,
    ( ( sk2 != sk2 )
    | ( sk2 = sk3 ) ),
    inference(replace_leibeq,[status(thm)],[92:[bind(A,$thf( (=) @ a @ sk2 ))]]) ).

thf(94,plain,
    ( ( sk2 != sk2 )
    | ( sk3 = sk2 ) ),
    inference(lifteq,[status(thm)],[93]) ).

thf(95,plain,
    sk3 = sk2,
    inference(pattern_uni,[status(thm)],[94:[]]) ).

thf(96,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[95,18]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SYO304^5 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n019.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 09:20:54 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.98/0.89  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.07/1.00  % [INFO] 	 Parsing done (111ms). 
% 1.07/1.01  % [INFO] 	 Running in sequential loop mode. 
% 1.71/1.22  % [INFO] 	 nitpick registered as external prover. 
% 1.71/1.22  % [INFO] 	 Scanning for conjecture ... 
% 1.73/1.26  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.73/1.28  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.73/1.28  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.73/1.29  % [INFO] 	 Type checking passed. 
% 1.73/1.29  % [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 ... 
% 3.71/1.96  % [INFO] 	 Killing All external provers ... 
% 3.71/1.96  % Time passed: 1441ms (effective reasoning time: 945ms)
% 3.71/1.96  % 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)>
% 3.71/1.96  % Axioms used in derivation (0): 
% 3.71/1.96  % No. of inferences in proof: 23
% 3.71/1.96  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1441 ms resp. 945 ms w/o parsing
% 3.71/2.00  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.71/2.00  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------