TSTP Solution File: SYN333+1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SYN333+1 : TPTP v8.2.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n025.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 08:18:04 EDT 2024

% Result   : Theorem 2.33s 1.61s
% Output   : Refutation 2.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   19 (   3 unt;   6 typ;   0 def)
%            Number of atoms       :   52 (   0 equ;   0 cnn)
%            Maximal formula atoms :    7 (   4 avg)
%            Number of connectives :  186 (  21   ~;  15   |;  16   &; 126   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :   31 (   0   ^  23   !;   8   ?;  31   :)

% Comments : 
%------------------------------------------------------------------------------
thf(big_f_type,type,
    big_f: $i > $i > $o ).

thf(big_g_type,type,
    big_g: $i > $i > $o ).

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

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

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

thf(sk4_type,type,
    sk4: $i > $i > $i ).

thf(1,conjecture,
    ? [A: $i,B: $i] :
    ! [C: $i] :
      ( ( big_f @ A @ B )
     => ( ( big_f @ B @ C )
        & ( big_f @ C @ C )
        & ( ( ( big_f @ A @ B )
            & ( big_g @ A @ B ) )
         => ( ( big_g @ A @ C )
            & ( big_g @ C @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_14_5) ).

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

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

thf(4,plain,
    ~ ( ! [A: $i,B: $i] : ( big_f @ A @ B )
     => ? [A: $i,B: $i] :
          ( ! [C: $i] : ( big_f @ B @ C )
          & ! [C: $i] : ( big_f @ C @ C )
          & ( ( ( big_f @ A @ B )
              & ( big_g @ A @ B ) )
           => ( ! [C: $i] : ( big_g @ A @ C )
              & ! [C: $i] : ( big_g @ C @ C ) ) ) ) ),
    inference(miniscope,[status(thm)],[3]) ).

thf(5,plain,
    ! [B: $i,A: $i] :
      ( ~ ( big_f @ B @ ( sk1 @ B @ A ) )
      | ~ ( big_f @ ( sk2 @ B @ A ) @ ( sk2 @ B @ A ) )
      | ~ ( big_g @ A @ ( sk3 @ B @ A ) )
      | ~ ( big_g @ ( sk4 @ B @ A ) @ ( sk4 @ B @ A ) ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(9,plain,
    ! [B: $i,A: $i] :
      ( ~ ( big_f @ B @ ( sk1 @ B @ A ) )
      | ~ ( big_f @ ( sk2 @ B @ A ) @ ( sk2 @ B @ A ) )
      | ~ ( big_g @ A @ ( sk3 @ B @ A ) )
      | ~ ( big_g @ ( sk4 @ B @ A ) @ ( sk4 @ B @ A ) ) ),
    inference(simp,[status(thm)],[5]) ).

thf(8,plain,
    ! [B: $i,A: $i] : ( big_f @ A @ B ),
    inference(cnf,[status(esa)],[4]) ).

thf(6,plain,
    ! [B: $i,A: $i] :
      ( ~ ( big_f @ B @ ( sk1 @ B @ A ) )
      | ~ ( big_f @ ( sk2 @ B @ A ) @ ( sk2 @ B @ A ) )
      | ( big_g @ A @ B ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(10,plain,
    ! [B: $i,A: $i] :
      ( ~ ( big_f @ B @ ( sk1 @ B @ A ) )
      | ~ ( big_f @ ( sk2 @ B @ A ) @ ( sk2 @ B @ A ) )
      | ( big_g @ A @ B ) ),
    inference(simp,[status(thm)],[6]) ).

thf(12,plain,
    ! [B: $i,A: $i] :
      ( ~ $true
      | ~ $true
      | ( big_g @ A @ B ) ),
    inference(rewrite,[status(thm)],[10,8]) ).

thf(13,plain,
    ! [B: $i,A: $i] : ( big_g @ A @ B ),
    inference(simp,[status(thm)],[12]) ).

thf(16,plain,
    ( ~ $true
    | ~ $true
    | ~ $true
    | ~ $true ),
    inference(rewrite,[status(thm)],[9,8,13]) ).

thf(17,plain,
    $false,
    inference(simp,[status(thm)],[16]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : SYN333+1 : TPTP v8.2.0. Released v2.0.0.
% 0.07/0.13  % Command  : run_Leo-III %s %d
% 0.12/0.33  % Computer : n025.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 : Mon May 20 14:23:39 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.81/0.79  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 0.93/0.90  % [INFO] 	 Parsing done (108ms). 
% 0.93/0.91  % [INFO] 	 Running in sequential loop mode. 
% 1.47/1.15  % [INFO] 	 nitpick registered as external prover. 
% 1.47/1.16  % [INFO] 	 Scanning for conjecture ... 
% 1.56/1.23  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.70/1.26  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.76/1.26  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.76/1.26  % [INFO] 	 Type checking passed. 
% 1.76/1.27  % [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 ... 
% 2.33/1.60  % [INFO] 	 Killing All external provers ... 
% 2.33/1.61  % Time passed: 1149ms (effective reasoning time: 693ms)
% 2.33/1.61  % 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)>
% 2.33/1.61  % Axioms used in derivation (0): 
% 2.33/1.61  % No. of inferences in proof: 13
% 2.33/1.61  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1149 ms resp. 693 ms w/o parsing
% 2.48/1.66  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.48/1.66  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------