TSTP Solution File: SYO221^5 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SYO221^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n012.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 08:56:09 EDT 2024

% Result   : Theorem 3.69s 2.28s
% Output   : Refutation 3.93s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   18 (   5 unt;   4 typ;   0 def)
%            Number of atoms       :   33 (  17 equ;   5 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   96 (  23   ~;   8   |;  12   &;  45   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   4 con; 0-2 aty)
%            Number of variables   :   18 (   0   ^  10   !;   8   ?;  18   :)

% Comments : 
%------------------------------------------------------------------------------
thf(b_type,type,
    b: $i ).

thf(cP_type,type,
    cP: $i > $o ).

thf(a_type,type,
    a: $i ).

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

thf(1,conjecture,
    ? [A: $i > $o] :
      ( ( ( cP @ a )
        & ( a != b ) )
     => ( ! [B: $i] :
            ( ( A @ B )
           => ( cP @ B ) )
        & ? [B: $i] : ( A @ B )
        & ~ ( A @ b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBLEDSOE6) ).

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

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

thf(4,plain,
    ~ ( ( ( cP @ a )
        & ( a != b ) )
     => ? [A: $i > $o] :
          ( ! [B: $i] :
              ( ( A @ B )
             => ( cP @ B ) )
          & ? [B: $i] : ( A @ B )
          & ~ ( A @ b ) ) ),
    inference(miniscope,[status(thm)],[3]) ).

thf(6,plain,
    ! [B: $i,A: $i > $o] :
      ( ~ ( cP @ ( sk1 @ A ) )
      | ~ ( A @ B )
      | ( A @ b ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(10,plain,
    ! [A: $i] :
      ( ~ ( cP @ ( sk1 @ ( (=) @ $i @ A ) ) )
      | ( A != A )
      | ( A = b ) ),
    inference(replace_leibeq,[status(thm)],[6:[bind(A,$thf( (=) @ $i @ B ))]]) ).

thf(11,plain,
    ! [A: $i] :
      ( ( A != A )
      | ( A = b )
      | ~ ( cP @ ( sk1 @ ( (=) @ $i @ A ) ) ) ),
    inference(lifteq,[status(thm)],[10]) ).

thf(12,plain,
    ! [A: $i] :
      ( ( A = b )
      | ~ ( cP @ ( sk1 @ ( (=) @ $i @ A ) ) ) ),
    inference(simp,[status(thm)],[11]) ).

thf(7,plain,
    a != b,
    inference(cnf,[status(esa)],[4]) ).

thf(15,plain,
    a != b,
    inference(lifteq,[status(thm)],[7]) ).

thf(21,plain,
    ! [A: $i] :
      ( ~ ( cP @ ( sk1 @ ( (=) @ $i @ A ) ) )
      | ( A != a ) ),
    inference(paramod_ordered,[status(thm)],[12,15]) ).

thf(22,plain,
    ~ ( cP @ ( sk1 @ ( (=) @ $i @ a ) ) ),
    inference(pattern_uni,[status(thm)],[21:[bind(A,$thf( a ))]]) ).

thf(8,plain,
    cP @ a,
    inference(cnf,[status(esa)],[4]) ).

thf(52,plain,
    $false,
    inference(e,[status(thm)],[22,12,3,8,15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem  : SYO221^5 : TPTP v8.2.0. Released v4.0.0.
% 0.02/0.11  % Command  : run_Leo-III %s %d
% 0.11/0.31  % Computer : n012.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Mon May 20 10:07:39 EDT 2024
% 0.11/0.31  % CPUTime  : 
% 1.01/0.93  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.30/1.08  % [INFO] 	 Parsing done (145ms). 
% 1.30/1.09  % [INFO] 	 Running in sequential loop mode. 
% 1.68/1.43  % [INFO] 	 eprover registered as external prover. 
% 1.68/1.44  % [INFO] 	 cvc4 registered as external prover. 
% 1.68/1.44  % [INFO] 	 Scanning for conjecture ... 
% 1.97/1.52  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.04/1.54  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.04/1.54  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.04/1.55  % [INFO] 	 Type checking passed. 
% 2.04/1.55  % [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 ... 
% 3.69/2.28  % External prover 'e' found a proof!
% 3.69/2.28  % [INFO] 	 Killing All external provers ... 
% 3.69/2.28  % Time passed: 1823ms (effective reasoning time: 1181ms)
% 3.69/2.28  % 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)>
% 3.69/2.28  % Axioms used in derivation (0): 
% 3.69/2.28  % No. of inferences in proof: 14
% 3.69/2.28  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1823 ms resp. 1181 ms w/o parsing
% 3.93/2.32  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.93/2.32  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------