TSTP Solution File: SEU974^5 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU974^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n020.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 03:40:34 EDT 2024

% Result   : Theorem 4.20s 2.03s
% Output   : Refutation 4.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    6
% Syntax   : Number of formulae    :    9 (   1 unt;   5 typ;   0 def)
%            Number of atoms       :   46 (  45 equ;   0 cnn)
%            Maximal formula atoms :   11 (  11 avg)
%            Number of connectives :  257 (   5   ~;   0   |;  39   &; 186   @)
%                                         (   0 <=>;  27  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (  14 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   13 (  13   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   54 (   0   ^  48   !;   6   ?;  54   :)

% Comments : 
%------------------------------------------------------------------------------
thf(a_type,type,
    a: $tType ).

thf(cR_type,type,
    cR: a > a ).

thf(cP_type,type,
    cP: a > a > a ).

thf(cL_type,type,
    cL: a > a ).

thf(cZ_type,type,
    cZ: a ).

thf(1,conjecture,
    ( ( ( ( cL @ cZ )
        = cZ )
      & ( ( cR @ cZ )
        = cZ )
      & ! [A: a,B: a] :
          ( ( cL @ ( cP @ A @ B ) )
          = A )
      & ! [A: a,B: a] :
          ( ( cR @ ( cP @ A @ B ) )
          = B )
      & ! [A: a] :
          ( ( A != cZ )
          = ( A
            = ( cP @ ( cL @ A ) @ ( cR @ A ) ) ) )
      & ! [A: a > $o] :
          ( ! [B: a,C: a] :
              ( ( A @ ( cP @ B @ C ) )
             => ( ( ( B = cZ )
                  = ( C = cZ ) )
                & ( A @ ( cP @ ( cL @ B ) @ ( cL @ C ) ) )
                & ( A @ ( cP @ ( cR @ B ) @ ( cR @ C ) ) ) ) )
         => ! [B: a,C: a] :
              ( ( A @ ( cP @ B @ C ) )
             => ( B = C ) ) ) )
   => ! [A: a,B: a] :
        ( ? [C: a > $o] :
            ( ( C @ ( cP @ A @ B ) )
            & ! [D: a,E: a] :
                ( ( C @ ( cP @ D @ E ) )
               => ( ( ( E = cZ )
                   => ( D = cZ ) )
                  & ( C @ ( cP @ ( cL @ D ) @ ( cL @ E ) ) )
                  & ( C @ ( cP @ ( cR @ D ) @ ( cR @ E ) ) ) ) ) )
       => ? [C: a > $o] :
            ( ( C @ ( cP @ ( cR @ A ) @ ( cR @ B ) ) )
            & ! [D: a,E: a] :
                ( ( C @ ( cP @ D @ E ) )
               => ( ( ( E = cZ )
                   => ( D = cZ ) )
                  & ( C @ ( cP @ ( cL @ D ) @ ( cL @ E ) ) )
                  & ( C @ ( cP @ ( cR @ D ) @ ( cR @ E ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cPU_LEM2C_pme) ).

thf(2,negated_conjecture,
    ~ ( ( ( ( cL @ cZ )
          = cZ )
        & ( ( cR @ cZ )
          = cZ )
        & ! [A: a,B: a] :
            ( ( cL @ ( cP @ A @ B ) )
            = A )
        & ! [A: a,B: a] :
            ( ( cR @ ( cP @ A @ B ) )
            = B )
        & ! [A: a] :
            ( ( A != cZ )
            = ( A
              = ( cP @ ( cL @ A ) @ ( cR @ A ) ) ) )
        & ! [A: a > $o] :
            ( ! [B: a,C: a] :
                ( ( A @ ( cP @ B @ C ) )
               => ( ( ( B = cZ )
                    = ( C = cZ ) )
                  & ( A @ ( cP @ ( cL @ B ) @ ( cL @ C ) ) )
                  & ( A @ ( cP @ ( cR @ B ) @ ( cR @ C ) ) ) ) )
           => ! [B: a,C: a] :
                ( ( A @ ( cP @ B @ C ) )
               => ( B = C ) ) ) )
     => ! [A: a,B: a] :
          ( ? [C: a > $o] :
              ( ( C @ ( cP @ A @ B ) )
              & ! [D: a,E: a] :
                  ( ( C @ ( cP @ D @ E ) )
                 => ( ( ( E = cZ )
                     => ( D = cZ ) )
                    & ( C @ ( cP @ ( cL @ D ) @ ( cL @ E ) ) )
                    & ( C @ ( cP @ ( cR @ D ) @ ( cR @ E ) ) ) ) ) )
         => ? [C: a > $o] :
              ( ( C @ ( cP @ ( cR @ A ) @ ( cR @ B ) ) )
              & ! [D: a,E: a] :
                  ( ( C @ ( cP @ D @ E ) )
                 => ( ( ( E = cZ )
                     => ( D = cZ ) )
                    & ( C @ ( cP @ ( cL @ D ) @ ( cL @ E ) ) )
                    & ( C @ ( cP @ ( cR @ D ) @ ( cR @ E ) ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ( ( ( cL @ cZ )
          = cZ )
        & ( ( cR @ cZ )
          = cZ )
        & ! [A: a,B: a] :
            ( ( cL @ ( cP @ A @ B ) )
            = A )
        & ! [A: a,B: a] :
            ( ( cR @ ( cP @ A @ B ) )
            = B )
        & ! [A: a] :
            ( ( A != cZ )
            = ( A
              = ( cP @ ( cL @ A ) @ ( cR @ A ) ) ) )
        & ! [A: a > $o] :
            ( ! [B: a,C: a] :
                ( ( A @ ( cP @ B @ C ) )
               => ( ( ( B = cZ )
                    = ( C = cZ ) )
                  & ( A @ ( cP @ ( cL @ B ) @ ( cL @ C ) ) )
                  & ( A @ ( cP @ ( cR @ B ) @ ( cR @ C ) ) ) ) )
           => ! [B: a,C: a] :
                ( ( A @ ( cP @ B @ C ) )
               => ( B = C ) ) ) )
     => ! [A: a,B: a] :
          ( ? [C: a > $o] :
              ( ( C @ ( cP @ A @ B ) )
              & ! [D: a,E: a] :
                  ( ( C @ ( cP @ D @ E ) )
                 => ( ( ( E = cZ )
                     => ( D = cZ ) )
                    & ( C @ ( cP @ ( cL @ D ) @ ( cL @ E ) ) )
                    & ( C @ ( cP @ ( cR @ D ) @ ( cR @ E ) ) ) ) ) )
         => ? [C: a > $o] :
              ( ( C @ ( cP @ ( cR @ A ) @ ( cR @ B ) ) )
              & ! [D: a,E: a] :
                  ( ( C @ ( cP @ D @ E ) )
                 => ( ( ( E = cZ )
                     => ( D = cZ ) )
                    & ( C @ ( cP @ ( cL @ D ) @ ( cL @ E ) ) )
                    & ( C @ ( cP @ ( cR @ D ) @ ( cR @ E ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(109,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU974^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n020.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 : Sun May 19 15:52:39 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 1.05/0.95  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.22/1.07  % [INFO] 	 Parsing done (122ms). 
% 1.22/1.08  % [INFO] 	 Running in sequential loop mode. 
% 1.70/1.28  % [INFO] 	 eprover registered as external prover. 
% 1.70/1.28  % [INFO] 	 cvc4 registered as external prover. 
% 1.70/1.28  % [INFO] 	 Scanning for conjecture ... 
% 1.95/1.35  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.95/1.38  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.95/1.38  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.95/1.38  % [INFO] 	 Type checking passed. 
% 1.95/1.38  % [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 ... 
% 4.20/2.03  % External prover 'e' found a proof!
% 4.20/2.03  % [INFO] 	 Killing All external provers ... 
% 4.20/2.03  % Time passed: 1486ms (effective reasoning time: 948ms)
% 4.20/2.03  % 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)>
% 4.20/2.03  % Axioms used in derivation (0): 
% 4.20/2.03  % No. of inferences in proof: 4
% 4.20/2.03  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1486 ms resp. 948 ms w/o parsing
% 4.20/2.06  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.20/2.06  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------