TSTP Solution File: SEU904^5 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU904^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n011.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 03:40:25 EDT 2024

% Result   : Theorem 3.46s 1.79s
% Output   : Refutation 3.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of formulae    :    7 (   1 unt;   3 typ;   0 def)
%            Number of atoms       :   10 (   9 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :  308 (   2   ~;   0   |;  57   &; 210   @)
%                                         (   0 <=>;  39  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (  17 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :   33 (  33   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    2 (   0 usr;   1 con; 0-2 aty)
%            Number of variables   :   87 (   0   ^  87   !;   0   ?;  87   :)

% Comments : 
%------------------------------------------------------------------------------
thf(g_type,type,
    g: $tType ).

thf(b_type,type,
    b: $tType ).

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

thf(1,conjecture,
    ! [A: g > b,B: b > a,C: g > $o,D: g > g > g,E: b > $o,F: b > b > b,G: a > $o,H: a > a > a] :
      ( ( ! [I: g,J: g] :
            ( ( ( C @ I )
              & ( C @ J ) )
           => ( C @ ( D @ I @ J ) ) )
        & ! [I: b,J: b] :
            ( ( ( E @ I )
              & ( E @ J ) )
           => ( E @ ( F @ I @ J ) ) )
        & ! [I: g] :
            ( ( C @ I )
           => ( E @ ( A @ I ) ) )
        & ! [I: g,J: g] :
            ( ( ( C @ I )
              & ( C @ J ) )
           => ( ( A @ ( D @ I @ J ) )
              = ( F @ ( A @ I ) @ ( A @ J ) ) ) )
        & ! [I: b,J: b] :
            ( ( ( E @ I )
              & ( E @ J ) )
           => ( E @ ( F @ I @ J ) ) )
        & ! [I: a,J: a] :
            ( ( ( G @ I )
              & ( G @ J ) )
           => ( G @ ( H @ I @ J ) ) )
        & ! [I: b] :
            ( ( E @ I )
           => ( G @ ( B @ I ) ) )
        & ! [I: b,J: b] :
            ( ( ( E @ I )
              & ( E @ J ) )
           => ( ( B @ ( F @ I @ J ) )
              = ( H @ ( B @ I ) @ ( B @ J ) ) ) ) )
     => ( ! [I: g,J: g] :
            ( ( ( C @ I )
              & ( C @ J ) )
           => ( C @ ( D @ I @ J ) ) )
        & ! [I: a,J: a] :
            ( ( ( G @ I )
              & ( G @ J ) )
           => ( G @ ( H @ I @ J ) ) )
        & ! [I: g] :
            ( ( C @ I )
           => ( G @ ( B @ ( A @ I ) ) ) )
        & ! [I: g,J: g] :
            ( ( ( C @ I )
              & ( C @ J ) )
           => ( ( B @ ( A @ ( D @ I @ J ) ) )
              = ( H @ ( B @ ( A @ I ) ) @ ( B @ ( A @ J ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM126_pme) ).

thf(2,negated_conjecture,
    ~ ! [A: g > b,B: b > a,C: g > $o,D: g > g > g,E: b > $o,F: b > b > b,G: a > $o,H: a > a > a] :
        ( ( ! [I: g,J: g] :
              ( ( ( C @ I )
                & ( C @ J ) )
             => ( C @ ( D @ I @ J ) ) )
          & ! [I: b,J: b] :
              ( ( ( E @ I )
                & ( E @ J ) )
             => ( E @ ( F @ I @ J ) ) )
          & ! [I: g] :
              ( ( C @ I )
             => ( E @ ( A @ I ) ) )
          & ! [I: g,J: g] :
              ( ( ( C @ I )
                & ( C @ J ) )
             => ( ( A @ ( D @ I @ J ) )
                = ( F @ ( A @ I ) @ ( A @ J ) ) ) )
          & ! [I: b,J: b] :
              ( ( ( E @ I )
                & ( E @ J ) )
             => ( E @ ( F @ I @ J ) ) )
          & ! [I: a,J: a] :
              ( ( ( G @ I )
                & ( G @ J ) )
             => ( G @ ( H @ I @ J ) ) )
          & ! [I: b] :
              ( ( E @ I )
             => ( G @ ( B @ I ) ) )
          & ! [I: b,J: b] :
              ( ( ( E @ I )
                & ( E @ J ) )
             => ( ( B @ ( F @ I @ J ) )
                = ( H @ ( B @ I ) @ ( B @ J ) ) ) ) )
       => ( ! [I: g,J: g] :
              ( ( ( C @ I )
                & ( C @ J ) )
             => ( C @ ( D @ I @ J ) ) )
          & ! [I: a,J: a] :
              ( ( ( G @ I )
                & ( G @ J ) )
             => ( G @ ( H @ I @ J ) ) )
          & ! [I: g] :
              ( ( C @ I )
             => ( G @ ( B @ ( A @ I ) ) ) )
          & ! [I: g,J: g] :
              ( ( ( C @ I )
                & ( C @ J ) )
             => ( ( B @ ( A @ ( D @ I @ J ) ) )
                = ( H @ ( B @ ( A @ I ) ) @ ( B @ ( A @ J ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ! [A: g > b,B: b > a,C: g > $o,D: g > g > g,E: b > $o,F: b > b > b,G: a > $o,H: a > a > a] :
        ( ( ! [I: g,J: g] :
              ( ( ( C @ I )
                & ( C @ J ) )
             => ( C @ ( D @ I @ J ) ) )
          & ! [I: b,J: b] :
              ( ( ( E @ I )
                & ( E @ J ) )
             => ( E @ ( F @ I @ J ) ) )
          & ! [I: g] :
              ( ( C @ I )
             => ( E @ ( A @ I ) ) )
          & ! [I: g,J: g] :
              ( ( ( C @ I )
                & ( C @ J ) )
             => ( ( A @ ( D @ I @ J ) )
                = ( F @ ( A @ I ) @ ( A @ J ) ) ) )
          & ! [I: b,J: b] :
              ( ( ( E @ I )
                & ( E @ J ) )
             => ( E @ ( F @ I @ J ) ) )
          & ! [I: a,J: a] :
              ( ( ( G @ I )
                & ( G @ J ) )
             => ( G @ ( H @ I @ J ) ) )
          & ! [I: b] :
              ( ( E @ I )
             => ( G @ ( B @ I ) ) )
          & ! [I: b,J: b] :
              ( ( ( E @ I )
                & ( E @ J ) )
             => ( ( B @ ( F @ I @ J ) )
                = ( H @ ( B @ I ) @ ( B @ J ) ) ) ) )
       => ( ! [I: g,J: g] :
              ( ( ( C @ I )
                & ( C @ J ) )
             => ( C @ ( D @ I @ J ) ) )
          & ! [I: a,J: a] :
              ( ( ( G @ I )
                & ( G @ J ) )
             => ( G @ ( H @ I @ J ) ) )
          & ! [I: g] :
              ( ( C @ I )
             => ( G @ ( B @ ( A @ I ) ) ) )
          & ! [I: g,J: g] :
              ( ( ( C @ I )
                & ( C @ J ) )
             => ( ( B @ ( A @ ( D @ I @ J ) ) )
                = ( H @ ( B @ ( A @ I ) ) @ ( B @ ( A @ J ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(35,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU904^5 : TPTP v8.2.0. Released v4.0.0.
% 0.16/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n011.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 : Sun May 19 18:05:09 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.94/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.32/0.97  % [INFO] 	 Parsing done (111ms). 
% 1.32/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.72/1.18  % [INFO] 	 eprover registered as external prover. 
% 1.72/1.19  % [INFO] 	 cvc4 registered as external prover. 
% 1.72/1.19  % [INFO] 	 Scanning for conjecture ... 
% 1.96/1.27  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.96/1.29  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.96/1.30  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.96/1.30  % [INFO] 	 Type checking passed. 
% 1.96/1.30  % [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 ... 
% 3.46/1.79  % External prover 'e' found a proof!
% 3.46/1.79  % [INFO] 	 Killing All external provers ... 
% 3.46/1.79  % Time passed: 1278ms (effective reasoning time: 811ms)
% 3.46/1.79  % 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)>
% 3.46/1.79  % Axioms used in derivation (0): 
% 3.46/1.79  % No. of inferences in proof: 4
% 3.46/1.79  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1278 ms resp. 811 ms w/o parsing
% 3.52/1.82  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.52/1.82  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------