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

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---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 : n009.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 18:39:43 EDT 2024

% Result   : Theorem 6.29s 2.25s
% Output   : Refutation 6.29s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   44 (   3 unt;  10 typ;   0 def)
%            Number of atoms       :  159 (  19 equ;   0 cnn)
%            Maximal formula atoms :    8 (   4 avg)
%            Number of connectives :  358 (  41   ~;  46   |;   7   &; 248   @)
%                                         (   0 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   7 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   37 (  37   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (   9 usr;   3 con; 0-3 aty)
%            Number of variables   :   56 (   0   ^  52   !;   2   ?;  56   :)
%                                         (   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(sk1_type,type,
    sk1: '\'type/realax/real\'' > $o ).

thf(sk2_type,type,
    sk2: '\'type/realax/real\'' ).

thf(sk3_type,type,
    sk3: ( '\'type/realax/real\'' > $o ) > $o ).

thf(sk4_type,type,
    sk4: '\'type/realax/real\'' > ( '\'type/realax/real\'' > $o ) > '\'type/realax/real\'' ).

thf(sk5_type,type,
    sk5: '\'type/realax/real\'' > ( '\'type/realax/real\'' > $o ) > '\'type/realax/real\'' ).

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(12,plain,
    ! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
      ( ~ ( sk3 @ A )
      | ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk5 @ B @ A ) @ A )
      | ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) ) ),
    inference(cnf,[status(esa)],[9]) ).

thf(18,plain,
    ! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
      ( ~ ( sk3 @ A )
      | ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk5 @ B @ A ) @ A )
      | ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) ) ),
    inference(simp,[status(thm)],[12]) ).

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(6,plain,
    ! [A: '\'type/realax/real\''] :
      ( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ sk1 )
      | ( '\'const/realax/real_le\'' @ sk2 @ A ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(10,plain,
    ! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
      ( ~ ( sk3 @ A )
      | ~ ( '\'const/realax/real_le\'' @ B @ ( sk5 @ B @ A ) )
      | ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) ) ),
    inference(cnf,[status(esa)],[9]) ).

thf(15,plain,
    ! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
      ( ~ ( sk3 @ A )
      | ~ ( '\'const/realax/real_le\'' @ B @ ( sk5 @ B @ A ) )
      | ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) ) ),
    inference(simp,[status(thm)],[10]) ).

thf(32,plain,
    ! [C: '\'type/realax/real\'',B: '\'type/realax/real\'' > $o,A: '\'type/realax/real\''] :
      ( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ sk1 )
      | ~ ( sk3 @ B )
      | ( '\'const/realax/real_le\'' @ C @ ( '\'const/sets/inf\'' @ B ) )
      | ( ( '\'const/realax/real_le\'' @ sk2 @ A )
       != ( '\'const/realax/real_le\'' @ C @ ( sk5 @ C @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[6,15]) ).

thf(33,plain,
    ! [A: '\'type/realax/real\'' > $o] :
      ( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk5 @ sk2 @ A ) @ sk1 )
      | ~ ( sk3 @ A )
      | ( '\'const/realax/real_le\'' @ sk2 @ ( '\'const/sets/inf\'' @ A ) ) ),
    inference(pattern_uni,[status(thm)],[32:[bind(A,$thf( sk5 @ sk2 @ E )),bind(B,$thf( E )),bind(C,$thf( sk2 ))]]) ).

thf(36,plain,
    ! [A: '\'type/realax/real\'' > $o] :
      ( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk5 @ sk2 @ A ) @ sk1 )
      | ~ ( sk3 @ A )
      | ( '\'const/realax/real_le\'' @ sk2 @ ( '\'const/sets/inf\'' @ A ) ) ),
    inference(simp,[status(thm)],[33]) ).

thf(274,plain,
    ! [C: '\'type/realax/real\'' > $o,B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
      ( ~ ( sk3 @ A )
      | ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) )
      | ~ ( sk3 @ C )
      | ( '\'const/realax/real_le\'' @ sk2 @ ( '\'const/sets/inf\'' @ C ) )
      | ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk5 @ B @ A ) @ A )
       != ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk5 @ sk2 @ C ) @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[18,36]) ).

thf(275,plain,
    ( ~ ( sk3 @ sk1 )
    | ( '\'const/realax/real_le\'' @ sk2 @ ( '\'const/sets/inf\'' @ sk1 ) )
    | ~ ( sk3 @ sk1 )
    | ( '\'const/realax/real_le\'' @ sk2 @ ( '\'const/sets/inf\'' @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[274:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk1 ))]]) ).

thf(287,plain,
    ( ~ ( sk3 @ sk1 )
    | ( '\'const/realax/real_le\'' @ sk2 @ ( '\'const/sets/inf\'' @ sk1 ) ) ),
    inference(simp,[status(thm)],[275]) ).

thf(5,plain,
    ~ ( '\'const/realax/real_le\'' @ sk2 @ ( '\'const/sets/inf\'' @ sk1 ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(11,plain,
    ! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
      ( ( A
        = ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
      | ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk4 @ B @ A ) @ A )
      | ( sk3 @ A ) ),
    inference(cnf,[status(esa)],[9]) ).

thf(19,plain,
    ! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
      ( ( A
        = ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
      | ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk4 @ B @ A ) @ A )
      | ( sk3 @ A ) ),
    inference(lifteq,[status(thm)],[11]) ).

thf(14,plain,
    ! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
      ( ( A
        = ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
      | ~ ( '\'const/realax/real_le\'' @ B @ ( sk4 @ B @ A ) )
      | ( sk3 @ A ) ),
    inference(cnf,[status(esa)],[9]) ).

thf(16,plain,
    ! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
      ( ( A
        = ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
      | ~ ( '\'const/realax/real_le\'' @ B @ ( sk4 @ B @ A ) )
      | ( sk3 @ A ) ),
    inference(lifteq,[status(thm)],[14]) ).

thf(7,plain,
    ( sk1
   != ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(8,plain,
    ( sk1
   != ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) ),
    inference(lifteq,[status(thm)],[7]) ).

thf(65,plain,
    ! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
      ( ~ ( '\'const/realax/real_le\'' @ B @ ( sk4 @ B @ A ) )
      | ( sk3 @ A )
      | ( A != sk1 ) ),
    inference(paramod_ordered,[status(thm)],[16,8]) ).

thf(66,plain,
    ! [A: '\'type/realax/real\''] :
      ( ~ ( '\'const/realax/real_le\'' @ A @ ( sk4 @ A @ sk1 ) )
      | ( sk3 @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[65:[bind(A,$thf( sk1 )),bind(B,$thf( B ))]]) ).

thf(79,plain,
    ! [A: '\'type/realax/real\''] :
      ( ~ ( '\'const/realax/real_le\'' @ A @ ( sk4 @ A @ sk1 ) )
      | ( sk3 @ sk1 ) ),
    inference(simp,[status(thm)],[66]) ).

thf(92,plain,
    ! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
      ( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ sk1 )
      | ( sk3 @ sk1 )
      | ( ( '\'const/realax/real_le\'' @ sk2 @ A )
       != ( '\'const/realax/real_le\'' @ B @ ( sk4 @ B @ sk1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[6,79]) ).

thf(93,plain,
    ( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk4 @ sk2 @ sk1 ) @ sk1 )
    | ( sk3 @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[92:[bind(A,$thf( sk4 @ sk2 @ sk1 )),bind(B,$thf( sk2 ))]]) ).

thf(222,plain,
    ! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
      ( ( A
        = ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
      | ( sk3 @ A )
      | ( sk3 @ sk1 )
      | ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk4 @ B @ A ) @ A )
       != ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk4 @ sk2 @ sk1 ) @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[19,93]) ).

thf(223,plain,
    ( ( sk1
      = ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
    | ( sk3 @ sk1 )
    | ( sk3 @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[222:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).

thf(233,plain,
    ( ( sk1
      = ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
    | ( sk3 @ sk1 ) ),
    inference(simp,[status(thm)],[223]) ).

thf(234,plain,
    sk3 @ sk1,
    inference(simplifyReflect,[status(thm)],[233,8]) ).

thf(310,plain,
    ( ~ $true
    | $false ),
    inference(rewrite,[status(thm)],[287,5,234]) ).

thf(311,plain,
    $false,
    inference(simp,[status(thm)],[310]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ANA086^1 : TPTP v8.2.0. Released v7.0.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n009.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 07:58:24 EDT 2024
% 0.15/0.37  % CPUTime  : 
% 0.83/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.18/0.95  % [INFO] 	 Parsing done (104ms). 
% 1.18/0.96  % [INFO] 	 Running in sequential loop mode. 
% 1.51/1.16  % [INFO] 	 nitpick registered as external prover. 
% 1.51/1.16  % [INFO] 	 Scanning for conjecture ... 
% 1.67/1.22  % [INFO] 	 Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ... 
% 1.67/1.24  % [INFO] 	 Axiom selection finished. Selected 1 axioms (removed 0 axioms). 
% 1.67/1.24  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.67/1.25  % [INFO] 	 Type checking passed. 
% 1.67/1.25  % [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 ... 
% 6.29/2.24  % [INFO] 	 Killing All external provers ... 
% 6.29/2.24  % Time passed: 1721ms (effective reasoning time: 1276ms)
% 6.29/2.24  % 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)>
% 6.29/2.25  % Axioms used in derivation (1): thm/sets/INF_
% 6.29/2.25  % No. of inferences in proof: 34
% 6.29/2.25  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1721 ms resp. 1276 ms w/o parsing
% 6.29/2.30  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.29/2.30  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------