TSTP Solution File: ANA086^1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ANA086^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n019.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 : Mon May 20 18:39:15 EDT 2024

% Result   : Theorem 3.03s 1.72s
% Output   : Refutation 3.03s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   11 (   1 unt;   5 typ;   0 def)
%            Number of atoms       :   34 (   5 equ;   0 cnn)
%            Maximal formula atoms :    8 (   5 avg)
%            Number of connectives :   97 (   7   ~;   0   |;   7   &;  67   @)
%                                         (   0 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   9 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   13 (  13   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4 usr;   1 con; 0-3 aty)
%            Number of variables   :   23 (   0   ^  19   !;   2   ?;  23   :)
%                                         (   2  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf('\'type/realax/real\'_type',type,
    '\'type/realax/real\'': $tType ).

thf('\'const/sets/inf\'_type',type,
    '\'const/sets/inf\'': ( '\'type/realax/real\'' > $o ) > '\'type/realax/real\'' ).

thf('\'const/sets/IN\'_type',type,
    '\'const/sets/IN\'': 
      !>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).

thf('\'const/sets/EMPTY\'_type',type,
    '\'const/sets/EMPTY\'': 
      !>[TA: $tType] : ( TA > $o ) ).

thf('\'const/realax/real_le\'_type',type,
    '\'const/realax/real_le\'': '\'type/realax/real\'' > '\'type/realax/real\'' > $o ).

thf(1,conjecture,
    ! [A: '\'type/realax/real\'' > $o,B: '\'type/realax/real\''] :
      ( ( ( A
         != ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
        & ! [C: '\'type/realax/real\''] :
            ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
           => ( '\'const/realax/real_le\'' @ B @ C ) ) )
     => ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/REAL_LE_INF_') ).

thf(2,negated_conjecture,
    ~ ! [A: '\'type/realax/real\'' > $o,B: '\'type/realax/real\''] :
        ( ( ( A
           != ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
          & ! [C: '\'type/realax/real\''] :
              ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
             => ( '\'const/realax/real_le\'' @ B @ C ) ) )
       => ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(4,plain,
    ~ ! [A: '\'type/realax/real\'' > $o,B: '\'type/realax/real\''] :
        ( ( ( A
           != ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
          & ! [C: '\'type/realax/real\''] :
              ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
             => ( '\'const/realax/real_le\'' @ B @ C ) ) )
       => ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(3,axiom,
    ! [A: '\'type/realax/real\'' > $o] :
      ( ( ( A
         != ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
        & ? [B: '\'type/realax/real\''] :
          ! [C: '\'type/realax/real\''] :
            ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
           => ( '\'const/realax/real_le\'' @ B @ C ) ) )
     => ( ! [B: '\'type/realax/real\''] :
            ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ B @ A )
           => ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ A ) @ B ) )
        & ! [B: '\'type/realax/real\''] :
            ( ! [C: '\'type/realax/real\''] :
                ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
               => ( '\'const/realax/real_le\'' @ B @ C ) )
           => ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/INF_') ).

thf(9,plain,
    ! [A: '\'type/realax/real\'' > $o] :
      ( ( ( A
         != ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
        & ? [B: '\'type/realax/real\''] :
          ! [C: '\'type/realax/real\''] :
            ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
           => ( '\'const/realax/real_le\'' @ B @ C ) ) )
     => ( ! [B: '\'type/realax/real\''] :
            ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ B @ A )
           => ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ A ) @ B ) )
        & ! [B: '\'type/realax/real\''] :
            ( ! [C: '\'type/realax/real\''] :
                ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
               => ( '\'const/realax/real_le\'' @ B @ C ) )
           => ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(21,plain,
    $false,
    inference(e,[status(thm)],[4,9]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : ANA086^1 : TPTP v8.2.0. Released v7.0.0.
% 0.15/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n019.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 : Mon May 20 07:58:24 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 1.00/0.90  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.36/1.03  % [INFO] 	 Parsing done (123ms). 
% 1.36/1.04  % [INFO] 	 Running in sequential loop mode. 
% 1.78/1.24  % [INFO] 	 eprover registered as external prover. 
% 1.78/1.25  % [INFO] 	 cvc4 registered as external prover. 
% 1.78/1.25  % [INFO] 	 Scanning for conjecture ... 
% 1.95/1.31  % [INFO] 	 Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ... 
% 1.95/1.33  % [INFO] 	 Axiom selection finished. Selected 1 axioms (removed 0 axioms). 
% 1.95/1.34  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.95/1.34  % [INFO] 	 Type checking passed. 
% 1.95/1.35  % [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 ... 
% 3.03/1.71  % External prover 'e' found a proof!
% 3.03/1.71  % [INFO] 	 Killing All external provers ... 
% 3.03/1.71  % Time passed: 1190ms (effective reasoning time: 676ms)
% 3.03/1.71  % 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)>
% 3.03/1.72  % Axioms used in derivation (1): thm/sets/INF_
% 3.03/1.72  % No. of inferences in proof: 6
% 3.03/1.72  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1190 ms resp. 676 ms w/o parsing
% 3.03/1.76  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.03/1.76  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------