TSTP Solution File: SYN057^5 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SYN057^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n022.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 08:17:18 EDT 2024

% Result   : Theorem 2.94s 1.67s
% Output   : Refutation 2.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   36 (  10 unt;   7 typ;   0 def)
%            Number of atoms       :  103 (   5 equ;   0 cnn)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives :  208 (  50   ~;  28   |;  18   &;  94   @)
%                                         (   0 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   33 (   0   ^  27   !;   6   ?;  33   :)

% Comments : 
%------------------------------------------------------------------------------
thf(cI_type,type,
    cI: $i > $o ).

thf(cJ_type,type,
    cJ: $i > $o ).

thf(cH_type,type,
    cH: $i > $o ).

thf(cG_type,type,
    cG: $i > $o ).

thf(cF_type,type,
    cF: $i > $o ).

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

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

thf(1,conjecture,
    ( ( ? [A: $i] :
          ( ( cF @ A )
          & ~ ( cG @ A ) )
      & ! [A: $i] :
          ( ( cF @ A )
         => ( cH @ A ) )
      & ! [A: $i] :
          ( ( ( cJ @ A )
            & ( cI @ A ) )
         => ( cF @ A ) )
      & ( ? [A: $i] :
            ( ( cH @ A )
            & ~ ( cG @ A ) )
       => ! [A: $i] :
            ( ( cI @ A )
           => ~ ( cH @ A ) ) ) )
   => ! [A: $i] :
        ( ( cJ @ A )
       => ~ ( cI @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cPELL27) ).

thf(2,negated_conjecture,
    ~ ( ( ? [A: $i] :
            ( ( cF @ A )
            & ~ ( cG @ A ) )
        & ! [A: $i] :
            ( ( cF @ A )
           => ( cH @ A ) )
        & ! [A: $i] :
            ( ( ( cJ @ A )
              & ( cI @ A ) )
           => ( cF @ A ) )
        & ( ? [A: $i] :
              ( ( cH @ A )
              & ~ ( cG @ A ) )
         => ! [A: $i] :
              ( ( cI @ A )
             => ~ ( cH @ A ) ) ) )
     => ! [A: $i] :
          ( ( cJ @ A )
         => ~ ( cI @ A ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ( ? [A: $i] :
            ( ( cF @ A )
            & ~ ( cG @ A ) )
        & ! [A: $i] :
            ( ( cF @ A )
           => ( cH @ A ) )
        & ! [A: $i] :
            ( ( ( cJ @ A )
              & ( cI @ A ) )
           => ( cF @ A ) )
        & ( ? [A: $i] :
              ( ( cH @ A )
              & ~ ( cG @ A ) )
         => ! [A: $i] :
              ( ( cI @ A )
             => ~ ( cH @ A ) ) ) )
     => ! [A: $i] :
          ( ( cJ @ A )
         => ~ ( cI @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(6,plain,
    cI @ sk2,
    inference(cnf,[status(esa)],[3]) ).

thf(9,plain,
    ! [A: $i] :
      ( ~ ( cJ @ A )
      | ~ ( cI @ A )
      | ( cF @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(11,plain,
    ! [A: $i] :
      ( ~ ( cJ @ A )
      | ~ ( cI @ A )
      | ( cF @ A ) ),
    inference(simp,[status(thm)],[9]) ).

thf(40,plain,
    ! [A: $i] :
      ( ~ ( cJ @ A )
      | ( cF @ A )
      | ( ( cI @ sk2 )
       != ( cI @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[6,11]) ).

thf(41,plain,
    ( ~ ( cJ @ sk2 )
    | ( cF @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[40:[bind(A,$thf( sk2 ))]]) ).

thf(7,plain,
    cJ @ sk2,
    inference(cnf,[status(esa)],[3]) ).

thf(48,plain,
    ( ~ $true
    | ( cF @ sk2 ) ),
    inference(rewrite,[status(thm)],[41,7]) ).

thf(49,plain,
    cF @ sk2,
    inference(simp,[status(thm)],[48]) ).

thf(5,plain,
    ! [A: $i] :
      ( ~ ( cF @ A )
      | ( cH @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(50,plain,
    ! [A: $i] :
      ( ( cH @ A )
      | ( ( cF @ sk2 )
       != ( cF @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[49,5]) ).

thf(51,plain,
    cH @ sk2,
    inference(pattern_uni,[status(thm)],[50:[bind(A,$thf( sk2 ))]]) ).

thf(8,plain,
    ! [B: $i,A: $i] :
      ( ~ ( cH @ A )
      | ( cG @ A )
      | ~ ( cI @ B )
      | ~ ( cH @ B ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(12,plain,
    ! [B: $i,A: $i] :
      ( ~ ( cH @ A )
      | ( cG @ A )
      | ~ ( cI @ B )
      | ~ ( cH @ B ) ),
    inference(simp,[status(thm)],[8]) ).

thf(10,plain,
    ~ ( cG @ sk1 ),
    inference(cnf,[status(esa)],[3]) ).

thf(13,plain,
    ! [B: $i,A: $i] :
      ( ~ ( cH @ A )
      | ~ ( cI @ B )
      | ~ ( cH @ B )
      | ( ( cG @ A )
       != ( cG @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[12,10]) ).

thf(14,plain,
    ! [A: $i] :
      ( ~ ( cH @ sk1 )
      | ~ ( cI @ A )
      | ~ ( cH @ A ) ),
    inference(pattern_uni,[status(thm)],[13:[bind(A,$thf( sk1 ))]]) ).

thf(20,plain,
    ! [A: $i] :
      ( ~ ( cH @ sk1 )
      | ~ ( cI @ A )
      | ~ ( cH @ A ) ),
    inference(simp,[status(thm)],[14]) ).

thf(21,plain,
    ! [A: $i] :
      ( ~ ( cH @ sk1 )
      | ~ ( cH @ A )
      | ( ( cI @ sk2 )
       != ( cI @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[6,20]) ).

thf(22,plain,
    ( ~ ( cH @ sk1 )
    | ~ ( cH @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[21:[bind(A,$thf( sk2 ))]]) ).

thf(4,plain,
    cF @ sk1,
    inference(cnf,[status(esa)],[3]) ).

thf(25,plain,
    ! [A: $i] :
      ( ( cH @ A )
      | ( ( cF @ sk1 )
       != ( cF @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4,5]) ).

thf(26,plain,
    cH @ sk1,
    inference(pattern_uni,[status(thm)],[25:[bind(A,$thf( sk1 ))]]) ).

thf(34,plain,
    ( ~ $true
    | ~ ( cH @ sk2 ) ),
    inference(rewrite,[status(thm)],[22,26]) ).

thf(35,plain,
    ~ ( cH @ sk2 ),
    inference(simp,[status(thm)],[34]) ).

thf(52,plain,
    $false,
    inference(rewrite,[status(thm)],[51,35]) ).

thf(53,plain,
    $false,
    inference(simp,[status(thm)],[52]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SYN057^5 : TPTP v8.2.0. Released v4.0.0.
% 0.14/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.37  % Computer : n022.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Mon May 20 15:37:39 EDT 2024
% 0.15/0.37  % CPUTime  : 
% 0.96/0.88  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.21/0.98  % [INFO] 	 Parsing done (99ms). 
% 1.21/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.62/1.18  % [INFO] 	 nitpick registered as external prover. 
% 1.62/1.18  % [INFO] 	 Scanning for conjecture ... 
% 1.74/1.24  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.80/1.26  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.80/1.26  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.80/1.26  % [INFO] 	 Type checking passed. 
% 1.80/1.26  % [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 ... 
% 2.94/1.67  % [INFO] 	 Killing All external provers ... 
% 2.94/1.67  % Time passed: 1125ms (effective reasoning time: 677ms)
% 2.94/1.67  % 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)>
% 2.94/1.67  % Axioms used in derivation (0): 
% 2.94/1.67  % No. of inferences in proof: 29
% 2.94/1.67  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1125 ms resp. 677 ms w/o parsing
% 2.94/1.72  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.94/1.72  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------