TSTP Solution File: SWW469+5 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SWW469+5 : TPTP v8.2.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n002.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 06:52:59 EDT 2024

% Result   : Theorem 6.19s 2.39s
% Output   : Refutation 6.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   25 (  11 unt;   7 typ;   0 def)
%            Number of atoms       :   29 (  18 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  114 (  22   ~;   4   |;   2   &;  81   @)
%                                         (   1 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   7 con; 0-2 aty)
%            Number of variables   :   21 (   0   ^  14   !;   7   ?;  21   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ti_type,type,
    ti: $i > $i > $i ).

thf(state_type,type,
    state: $i ).

thf(hBOOL_type,type,
    hBOOL: $i > $o ).

thf(hoare_1883395792gleton_type,type,
    hoare_1883395792gleton: $i ).

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

thf(sk8_type,type,
    sk8: $i ).

thf(sk9_type,type,
    sk9: $i ).

thf(1,conjecture,
    ! [A: $i] :
      ~ ! [B: $i] :
          ( ( ti @ state @ B )
          = ( ti @ state @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] :
        ~ ! [B: $i] :
            ( ( ti @ state @ B )
            = ( ti @ state @ A ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(65,plain,
    ~ ! [A: $i] :
        ~ ! [B: $i] :
            ( ( ti @ state @ B )
            = ( ti @ state @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(66,plain,
    ~ ~ ? [A: $i] :
        ! [B: $i] :
          ( ( ti @ state @ B )
          = ( ti @ state @ A ) ),
    inference(miniscope,[status(thm)],[65]) ).

thf(67,plain,
    ! [A: $i] :
      ( ( ti @ state @ A )
      = ( ti @ state @ sk1 ) ),
    inference(cnf,[status(esa)],[66]) ).

thf(68,plain,
    ! [A: $i] :
      ( ( ti @ state @ A )
      = ( ti @ state @ sk1 ) ),
    inference(lifteq,[status(thm)],[67]) ).

thf(48,axiom,
    ( ( hBOOL @ hoare_1883395792gleton )
  <=> ? [A: $i,B: $i] :
        ( ( ti @ state @ A )
       != ( ti @ state @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_state__not__singleton__def) ).

thf(192,plain,
    ( ( ( hBOOL @ hoare_1883395792gleton )
     => ? [A: $i,B: $i] :
          ( ( ti @ state @ A )
         != ( ti @ state @ B ) ) )
    & ( ? [A: $i,B: $i] :
          ( ( ti @ state @ A )
         != ( ti @ state @ B ) )
     => ( hBOOL @ hoare_1883395792gleton ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(193,plain,
    ( ( ( hBOOL @ hoare_1883395792gleton )
     => ~ ! [A: $i,B: $i] :
            ( ( ti @ state @ A )
            = ( ti @ state @ B ) ) )
    & ( ~ ! [A: $i,B: $i] :
            ( ( ti @ state @ A )
            = ( ti @ state @ B ) )
     => ( hBOOL @ hoare_1883395792gleton ) ) ),
    inference(miniscope,[status(thm)],[192]) ).

thf(195,plain,
    ( ~ ( hBOOL @ hoare_1883395792gleton )
    | ( ( ti @ state @ sk8 )
     != ( ti @ state @ sk9 ) ) ),
    inference(cnf,[status(esa)],[193]) ).

thf(197,plain,
    ( ( ( ti @ state @ sk9 )
     != ( ti @ state @ sk8 ) )
    | ~ ( hBOOL @ hoare_1883395792gleton ) ),
    inference(lifteq,[status(thm)],[195]) ).

thf(3,axiom,
    hBOOL @ hoare_1883395792gleton,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(69,plain,
    hBOOL @ hoare_1883395792gleton,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(265,plain,
    ( ( ( ti @ state @ sk9 )
     != ( ti @ state @ sk8 ) )
    | ~ $true ),
    inference(rewrite,[status(thm)],[197,69]) ).

thf(266,plain,
    ( ( ti @ state @ sk9 )
   != ( ti @ state @ sk8 ) ),
    inference(simp,[status(thm)],[265]) ).

thf(271,plain,
    ! [A: $i] :
      ( ( ( ti @ state @ sk8 )
       != ( ti @ state @ sk1 ) )
      | ( ( ti @ state @ A )
       != ( ti @ state @ sk9 ) ) ),
    inference(paramod_ordered,[status(thm)],[68,266]) ).

thf(272,plain,
    ( ( ti @ state @ sk8 )
   != ( ti @ state @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[271:[bind(A,$thf( sk9 ))]]) ).

thf(292,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[272,68]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SWW469+5 : TPTP v8.2.0. Released v5.3.0.
% 0.16/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n002.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Sat May 18 19:33:09 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.99/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.51/1.04  % [INFO] 	 Parsing done (165ms). 
% 1.51/1.05  % [INFO] 	 Running in sequential loop mode. 
% 1.94/1.24  % [INFO] 	 nitpick registered as external prover. 
% 1.94/1.25  % [INFO] 	 Scanning for conjecture ... 
% 2.19/1.33  % [INFO] 	 Found a conjecture (or negated_conjecture) and 62 axioms. Running axiom selection ... 
% 2.34/1.39  % [INFO] 	 Axiom selection finished. Selected 62 axioms (removed 0 axioms). 
% 2.93/1.50  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.93/1.51  % [INFO] 	 Type checking passed. 
% 2.93/1.51  % [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 ... 
% 6.19/2.39  % [INFO] 	 Killing All external provers ... 
% 6.19/2.39  % Time passed: 1847ms (effective reasoning time: 1336ms)
% 6.19/2.39  % 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)>
% 6.19/2.39  % Axioms used in derivation (2): fact_0_state__not__singleton__def, conj_0
% 6.19/2.39  % No. of inferences in proof: 18
% 6.19/2.39  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1847 ms resp. 1336 ms w/o parsing
% 6.36/2.41  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.36/2.41  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------