TSTP Solution File: SEV181^5 by Leo-III---1.7.15

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : SEV181^5 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d THM

% Computer : n027.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 : Mon Jun 24 15:58:26 EDT 2024

% Result   : Theorem 6.45s 2.29s
% Output   : Refutation 6.45s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   22 (  11 unt;   0 typ;   1 def)
%            Number of atoms       :   59 (  32 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  134 (  23   ~;  10   |;  10   &;  85   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   34 (  34   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4 usr;   1 con; 0-2 aty)
%            Number of variables   :   41 (   8   ^  23   !;  10   ?;  41   :)

% Comments : 
%------------------------------------------------------------------------------
thf(cD_FOR_X5309_type,type,
    cD_FOR_X5309: ( ( $i > $o ) > $i ) > $i > $o ).

thf(cD_FOR_X5309_def,definition,
    ( cD_FOR_X5309
    = ( ^ [A: ( $i > $o ) > $i,B: $i] :
        ? [C: $i > $o] :
          ( ~ ( C @ ( A @ C ) )
          & ( B
            = ( A @ C ) ) ) ) ) ).

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

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

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

thf(1,conjecture,
    ! [A: ( $i > $o ) > $i] :
      ( ! [B: $i > $o,C: $i > $o] :
          ( ( ( A @ B )
            = ( A @ C ) )
         => ( B = C ) )
     => ~ ( cD_FOR_X5309 @ A @ ( A @ ( cD_FOR_X5309 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM143C_pme) ).

thf(2,negated_conjecture,
    ~ ! [A: ( $i > $o ) > $i] :
        ( ! [B: $i > $o,C: $i > $o] :
            ( ( ( A @ B )
              = ( A @ C ) )
           => ( B = C ) )
       => ~ ( cD_FOR_X5309 @ A @ ( A @ ( cD_FOR_X5309 @ A ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(4,plain,
    ( ( sk1
      @ ^ [A: $i] :
        ? [B: $i > $o] :
          ( ~ ( B @ ( sk1 @ B ) )
          & ( A
            = ( sk1 @ B ) ) ) )
    = ( sk1 @ sk2 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(7,plain,
    ( ( sk1
      @ ^ [A: $i] :
        ? [B: $i > $o] :
          ( ~ ( B @ ( sk1 @ B ) )
          & ( A
            = ( sk1 @ B ) ) ) )
    = ( sk1 @ sk2 ) ),
    inference(lifteq,[status(thm)],[4]) ).

thf(6,plain,
    ! [B: $i > $o,A: $i > $o] :
      ( ( ( sk1 @ A )
       != ( sk1 @ B ) )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(8,plain,
    ! [B: $i > $o,A: $i > $o] :
      ( ( ( sk1 @ A )
       != ( sk1 @ B ) )
      | ( A = B ) ),
    inference(lifteq,[status(thm)],[6]) ).

thf(9,plain,
    ! [A: $i > $o] :
      ( ( sk3 @ ( sk1 @ A ) )
      = A ),
    introduced(tautology,[new_symbols(inverse(sk1),[sk3])]) ).

thf(19,plain,
    ! [A: $i > $o] :
      ( ( ( sk3 @ ( sk1 @ sk2 ) )
        = A )
      | ( ( sk1
          @ ^ [B: $i] :
            ? [C: $i > $o] :
              ( ~ ( C @ ( sk1 @ C ) )
              & ( B
                = ( sk1 @ C ) ) ) )
       != ( sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[7,9]) ).

thf(20,plain,
    ( ( sk3 @ ( sk1 @ sk2 ) )
    = ( ^ [A: $i] :
        ? [B: $i > $o] :
          ( ~ ( B @ ( sk1 @ B ) )
          & ( A
            = ( sk1 @ B ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[19:[bind(A,$thf( ^ [B: $i] : ? [C: $i > $o] : ( ~ ( C @ ( sk1 @ C ) ) & ( B = ( sk1 @ C ) ) ) ))]]) ).

thf(25,plain,
    ( sk2
    = ( ^ [A: $i] :
        ? [B: $i > $o] :
          ( ~ ( B @ ( sk1 @ B ) )
          & ( A
            = ( sk1 @ B ) ) ) ) ),
    inference(rewrite,[status(thm)],[20,9]) ).

thf(26,plain,
    ! [A: $i] :
      ( ( sk2 @ A )
      = ( ? [B: $i > $o] :
            ( ~ ( B @ ( sk1 @ B ) )
            & ( A
              = ( sk1 @ B ) ) ) ) ),
    inference(func_ext,[status(esa)],[25]) ).

thf(88,plain,
    ! [A: $i] :
      ( ( sk2 @ A )
      | ~ ? [B: $i > $o] :
            ( ~ ( B @ ( sk1 @ B ) )
            & ( A
              = ( sk1 @ B ) ) ) ),
    inference(bool_ext,[status(thm)],[26]) ).

thf(96,plain,
    ! [B: $i > $o,A: $i] :
      ( ( B @ ( sk1 @ B ) )
      | ( A
       != ( sk1 @ B ) )
      | ( sk2 @ A ) ),
    inference(cnf,[status(esa)],[88]) ).

thf(97,plain,
    ! [B: $i > $o,A: $i] :
      ( ( A
       != ( sk1 @ B ) )
      | ( B @ ( sk1 @ B ) )
      | ( sk2 @ A ) ),
    inference(lifteq,[status(thm)],[96]) ).

thf(98,plain,
    ! [A: $i > $o] :
      ( ( A @ ( sk1 @ A ) )
      | ( sk2 @ ( sk1 @ A ) ) ),
    inference(simp,[status(thm)],[97]) ).

thf(5,plain,
    ~ ( sk2 @ ( sk1 @ sk2 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(204,plain,
    ! [A: $i > $o] :
      ( ( A @ ( sk1 @ A ) )
      | ( ( sk2 @ ( sk1 @ A ) )
       != ( sk2 @ ( sk1 @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[98,5]) ).

thf(205,plain,
    sk2 @ ( sk1 @ sk2 ),
    inference(pattern_uni,[status(thm)],[204:[bind(A,$thf( sk2 ))]]) ).

thf(287,plain,
    $false,
    inference(rewrite,[status(thm)],[205,5]) ).

thf(288,plain,
    $false,
    inference(simp,[status(thm)],[287]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEV181^5 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.07/0.12  % Command  : run_Leo-III %s %d THM
% 0.12/0.33  % Computer : n027.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Fri Jun 21 19:38:25 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 0.97/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.18/0.96  % [INFO] 	 Parsing done (96ms). 
% 1.18/0.96  % [INFO] 	 Running in sequential loop mode. 
% 1.41/1.16  % [INFO] 	 eprover registered as external prover. 
% 1.41/1.17  % [INFO] 	 Scanning for conjecture ... 
% 1.74/1.22  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.74/1.24  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.74/1.24  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.74/1.24  % [INFO] 	 Type checking passed. 
% 1.74/1.24  % [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 ... 
% 6.45/2.29  % [INFO] 	 Killing All external provers ... 
% 6.45/2.29  % Time passed: 1763ms (effective reasoning time: 1325ms)
% 6.45/2.29  % 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)>
% 6.45/2.29  % Axioms used in derivation (0): 
% 6.45/2.29  % No. of inferences in proof: 21
% 6.45/2.29  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1763 ms resp. 1325 ms w/o parsing
% 6.45/2.32  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.45/2.32  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------