TSTP Solution File: SET557^1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SET557^1 : TPTP v8.2.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n028.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 03:06:14 EDT 2024

% Result   : Theorem 7.42s 2.65s
% Output   : Refutation 7.42s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   17 (  11 unt;   2 typ;   0 def)
%            Number of atoms       :   28 (   9 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   75 (  19   ~;   6   |;   0   &;  50   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   23 (  23   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   2 usr;   2 con; 0-2 aty)
%            Number of variables   :   28 (   4   ^  16   !;   8   ?;  28   :)

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

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

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

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

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

thf(4,plain,
    ? [A: $i > $i > $o] :
    ! [B: $i > $o] :
    ? [C: $i] :
      ( ( A @ C )
      = B ),
    inference(polarity_switch,[status(thm)],[3]) ).

thf(5,plain,
    ! [A: $i > $o] :
      ( ( sk1 @ ( sk2 @ A ) )
      = A ),
    inference(cnf,[status(esa)],[4]) ).

thf(6,plain,
    ! [A: $i > $o] :
      ( ( sk1 @ ( sk2 @ A ) )
      = A ),
    inference(lifteq,[status(thm)],[5]) ).

thf(7,plain,
    ! [B: $i,A: $i > $o] :
      ( ( sk1 @ ( sk2 @ A ) @ B )
      = ( A @ B ) ),
    inference(func_ext,[status(esa)],[6]) ).

thf(9,plain,
    ! [B: $i,A: $i > $o] :
      ( ( sk1 @ ( sk2 @ A ) @ B )
      | ~ ( A @ B ) ),
    inference(bool_ext,[status(thm)],[7]) ).

thf(250,plain,
    ! [B: $i,A: $i > $o] :
      ( ( sk1 @ ( sk2 @ A ) @ B )
      | ( ( A @ B )
       != ( ~ ( sk1 @ ( sk2 @ A ) @ B ) ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[9]) ).

thf(270,plain,
    ( sk1
    @ ( sk2
      @ ^ [A: $i] :
          ~ ( sk1 @ A @ A ) )
    @ ( sk2
      @ ^ [A: $i] :
          ~ ( sk1 @ A @ A ) ) ),
    inference(pre_uni,[status(thm)],[250:[bind(A,$thf( ^ [C: $i] : ~ ( sk1 @ C @ C ) )),bind(B,$thf( sk2 @ ^ [C: $i] : ~ ( sk1 @ C @ C ) ))]]) ).

thf(8,plain,
    ! [B: $i,A: $i > $o] :
      ( ~ ( sk1 @ ( sk2 @ A ) @ B )
      | ( A @ B ) ),
    inference(bool_ext,[status(thm)],[7]) ).

thf(18,plain,
    ! [B: $i,A: $i > $o] :
      ( ~ ( sk1 @ ( sk2 @ A ) @ B )
      | ( ( A @ B )
       != ( ~ ( sk1 @ ( sk2 @ A ) @ B ) ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[8]) ).

thf(32,plain,
    ~ ( sk1
      @ ( sk2
        @ ^ [A: $i] :
            ~ ( sk1 @ A @ A ) )
      @ ( sk2
        @ ^ [A: $i] :
            ~ ( sk1 @ A @ A ) ) ),
    inference(pre_uni,[status(thm)],[18:[bind(A,$thf( ^ [C: $i] : ~ ( sk1 @ C @ C ) )),bind(B,$thf( sk2 @ ^ [C: $i] : ~ ( sk1 @ C @ C ) ))]]) ).

thf(372,plain,
    $false,
    inference(rewrite,[status(thm)],[270,32]) ).

thf(373,plain,
    $false,
    inference(simp,[status(thm)],[372]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem  : SET557^1 : TPTP v8.2.0. Released v3.6.0.
% 0.02/0.13  % Command  : run_Leo-III %s %d
% 0.13/0.32  % Computer : n028.cluster.edu
% 0.13/0.32  % Model    : x86_64 x86_64
% 0.13/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32  % Memory   : 8042.1875MB
% 0.13/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32  % CPULimit : 300
% 0.13/0.32  % WCLimit  : 300
% 0.13/0.32  % DateTime : Mon May 20 11:08:38 EDT 2024
% 0.13/0.32  % CPUTime  : 
% 0.95/0.89  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.21/1.03  % [INFO] 	 Parsing done (140ms). 
% 1.21/1.04  % [INFO] 	 Running in sequential loop mode. 
% 1.65/1.38  % [INFO] 	 nitpick registered as external prover. 
% 1.65/1.39  % [INFO] 	 Scanning for conjecture ... 
% 1.80/1.46  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.92/1.49  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.92/1.49  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.92/1.49  % [INFO] 	 Type checking passed. 
% 1.92/1.50  % [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 ... 
% 7.42/2.64  % [INFO] 	 Killing All external provers ... 
% 7.42/2.65  % Time passed: 2198ms (effective reasoning time: 1599ms)
% 7.42/2.65  % 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)>
% 7.42/2.65  % Axioms used in derivation (0): 
% 7.42/2.65  % No. of inferences in proof: 15
% 7.42/2.65  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2198 ms resp. 1599 ms w/o parsing
% 7.42/2.70  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.42/2.70  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------