TSTP Solution File: NUN088+1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : NUN088+1 : TPTP v8.2.0. Released v7.3.0.
% 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 02:16:43 EDT 2024

% Result   : Theorem 3.66s 1.87s
% Output   : Refutation 3.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   21 (   6 unt;   6 typ;   0 def)
%            Number of atoms       :   36 (   1 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  102 (  31   ~;  19   |;   0   &;  52   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :   24 (   0   ^  24   !;   0   ?;  24   :)

% Comments : 
%------------------------------------------------------------------------------
thf(id_type,type,
    id: $i > $i > $o ).

thf(r1_type,type,
    r1: $i > $o ).

thf(r2_type,type,
    r2: $i > $i > $o ).

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

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

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

thf(1,conjecture,
    ! [A: $i] :
      ( ! [B: $i] :
          ( ~ ( id @ B @ A )
          | ~ ( r1 @ B ) )
      | ! [B: $i] :
          ( ~ ( r1 @ B )
          | ~ ( r2 @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zerounidone) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] :
        ( ! [B: $i] :
            ( ~ ( id @ B @ A )
            | ~ ( r1 @ B ) )
        | ! [B: $i] :
            ( ~ ( r1 @ B )
            | ~ ( r2 @ B @ A ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(21,plain,
    ~ ! [A: $i] :
        ( ! [B: $i] :
            ( ~ ( id @ B @ A )
            | ~ ( r1 @ B ) )
        | ! [B: $i] :
            ( ~ ( r1 @ B )
            | ~ ( r2 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(22,plain,
    r2 @ sk3 @ sk1,
    inference(cnf,[status(esa)],[21]) ).

thf(25,plain,
    id @ sk2 @ sk1,
    inference(cnf,[status(esa)],[21]) ).

thf(9,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ~ ( id @ C @ B )
          | ~ ( r1 @ C ) )
      | ~ ( r2 @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7a) ).

thf(52,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ~ ( id @ C @ B )
          | ~ ( r1 @ C ) )
      | ~ ( r2 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(53,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( id @ C @ B )
      | ~ ( r1 @ C )
      | ~ ( r2 @ A @ B ) ),
    inference(cnf,[status(esa)],[52]) ).

thf(112,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( r1 @ C )
      | ~ ( r2 @ A @ B )
      | ( ( id @ sk2 @ sk1 )
       != ( id @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[25,53]) ).

thf(113,plain,
    ! [A: $i] :
      ( ~ ( r1 @ sk2 )
      | ~ ( r2 @ A @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[112:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( sk2 ))]]) ).

thf(24,plain,
    r1 @ sk2,
    inference(cnf,[status(esa)],[21]) ).

thf(115,plain,
    ! [A: $i] :
      ( ~ $true
      | ~ ( r2 @ A @ sk1 ) ),
    inference(rewrite,[status(thm)],[113,24]) ).

thf(116,plain,
    ! [A: $i] :
      ~ ( r2 @ A @ sk1 ),
    inference(simp,[status(thm)],[115]) ).

thf(117,plain,
    $false,
    inference(rewrite,[status(thm)],[22,116]) ).

thf(118,plain,
    $false,
    inference(simp,[status(thm)],[117]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : NUN088+1 : TPTP v8.2.0. Released v7.3.0.
% 0.12/0.15  % 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 : Sat May 18 14:52:09 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.97/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.15/0.99  % [INFO] 	 Parsing done (126ms). 
% 1.15/1.00  % [INFO] 	 Running in sequential loop mode. 
% 1.77/1.21  % [INFO] 	 nitpick registered as external prover. 
% 1.77/1.22  % [INFO] 	 Scanning for conjecture ... 
% 1.90/1.27  % [INFO] 	 Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ... 
% 1.90/1.31  % [INFO] 	 Axiom selection finished. Selected 18 axioms (removed 0 axioms). 
% 2.22/1.36  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.22/1.36  % [INFO] 	 Type checking passed. 
% 2.22/1.36  % [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 ... 
% 3.66/1.86  % [INFO] 	 Killing All external provers ... 
% 3.66/1.87  % Time passed: 1333ms (effective reasoning time: 857ms)
% 3.66/1.87  % 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)>
% 3.66/1.87  % Axioms used in derivation (1): axiom_7a
% 3.66/1.87  % No. of inferences in proof: 15
% 3.66/1.87  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1333 ms resp. 857 ms w/o parsing
% 3.66/1.89  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.66/1.89  % [INFO] 	 Killing All external provers ... 
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