TSTP Solution File: LCL864^1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : LCL864^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n015.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 00:08:34 EDT 2024

% Result   : Theorem 3.91s 1.92s
% Output   : Refutation 3.91s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   15 (   9 unt;   6 typ;   5 def)
%            Number of atoms       :   26 (   8 equ;   0 cnn)
%            Maximal formula atoms :    1 (   2 avg)
%            Number of connectives :   84 (   2   ~;   0   |;  17   &;  58   @)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   2 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   31 (  31   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5 usr;   1 con; 0-2 aty)
%            Number of variables   :   33 (   5   ^  26   !;   2   ?;  33   :)

% Comments : 
%------------------------------------------------------------------------------
thf(mu_type,type,
    mu: $tType ).

thf(mreflexive_type,type,
    mreflexive: ( $i > $i > $o ) > $o ).

thf(mreflexive_def,definition,
    ( mreflexive
    = ( ^ [A: $i > $i > $o] :
        ! [B: $i] : ( A @ B @ B ) ) ) ).

thf(msymmetric_type,type,
    msymmetric: ( $i > $i > $o ) > $o ).

thf(msymmetric_def,definition,
    ( msymmetric
    = ( ^ [A: $i > $i > $o] :
        ! [B: $i,C: $i] :
          ( ( A @ B @ C )
         => ( A @ C @ B ) ) ) ) ).

thf(mserial_type,type,
    mserial: ( $i > $i > $o ) > $o ).

thf(mserial_def,definition,
    ( mserial
    = ( ^ [A: $i > $i > $o] :
        ! [B: $i] :
        ? [C: $i] : ( A @ B @ C ) ) ) ).

thf(mtransitive_type,type,
    mtransitive: ( $i > $i > $o ) > $o ).

thf(mtransitive_def,definition,
    ( mtransitive
    = ( ^ [A: $i > $i > $o] :
        ! [B: $i,C: $i,D: $i] :
          ( ( ( A @ B @ C )
            & ( A @ C @ D ) )
         => ( A @ B @ D ) ) ) ) ).

thf(meuclidean_type,type,
    meuclidean: ( $i > $i > $o ) > $o ).

thf(meuclidean_def,definition,
    ( meuclidean
    = ( ^ [A: $i > $i > $o] :
        ! [B: $i,C: $i,D: $i] :
          ( ( ( A @ B @ C )
            & ( A @ B @ D ) )
         => ( A @ C @ D ) ) ) ) ).

thf(1,conjecture,
    ! [A: $i > $i > $o] :
      ( ( ( mreflexive @ A )
        & ( meuclidean @ A ) )
      = ( ( mserial @ A )
        & ( mtransitive @ A )
        & ( msymmetric @ A )
        & ( meuclidean @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).

thf(2,negated_conjecture,
    ~ ! [A: $i > $i > $o] :
        ( ( ( mreflexive @ A )
          & ( meuclidean @ A ) )
        = ( ( mserial @ A )
          & ( mtransitive @ A )
          & ( msymmetric @ A )
          & ( meuclidean @ A ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(50,plain,
    $false,
    inference(cvc4,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : LCL864^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% 0.12/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n015.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Mon May 20 01:04:09 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 1.00/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.32/1.07  % [INFO] 	 Parsing done (151ms). 
% 1.32/1.08  % [INFO] 	 Running in sequential loop mode. 
% 1.86/1.29  % [INFO] 	 eprover registered as external prover. 
% 1.86/1.29  % [INFO] 	 cvc4 registered as external prover. 
% 1.86/1.29  % [INFO] 	 Scanning for conjecture ... 
% 2.23/1.40  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.23/1.42  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.23/1.42  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.23/1.42  % [INFO] 	 Type checking passed. 
% 2.23/1.42  % [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 ... 
% 3.91/1.92  % External prover 'cvc4' found a proof!
% 3.91/1.92  % [INFO] 	 Killing All external provers ... 
% 3.91/1.92  % Time passed: 1390ms (effective reasoning time: 837ms)
% 3.91/1.92  % 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)>
% 3.91/1.92  % Axioms used in derivation (0): 
% 3.91/1.92  % No. of inferences in proof: 4
% 3.91/1.92  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1390 ms resp. 837 ms w/o parsing
% 3.91/1.95  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.91/1.95  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------