TSTP Solution File: ANA092^1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : ANA092^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n016.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 18:39:44 EDT 2024

% Result   : Theorem 135.32s 22.40s
% Output   : Refutation 135.32s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   87 (   5 unt;  12 typ;   0 def)
%            Number of atoms       :  385 (  33 equ;   0 cnn)
%            Maximal formula atoms :    8 (   5 avg)
%            Number of connectives :  808 (  82   ~; 100   |;   9   &; 592   @)
%                                         (   0 <=>;  25  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   7 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   38 (  38   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  11 usr;   5 con; 0-3 aty)
%            Number of variables   :  105 (   0   ^  98   !;   5   ?; 105   :)
%                                         (   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\'' ).

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

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

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

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

thf(sk6_type,type,
    sk6: '\'type/realax/real\'' > ( '\'type/realax/real\'' > $o ) > '\'type/realax/real\'' ).

thf(sk8_type,type,
    sk8: '\'type/realax/real\'' ).

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

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

thf(5,plain,
    ~ ! [A: '\'type/realax/real\'',B: '\'type/realax/real\'' > $o] :
        ( ( ( B
           != ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
          & ? [C: '\'type/realax/real\''] :
            ! [D: '\'type/realax/real\''] :
              ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ D @ B )
             => ( '\'const/realax/real_le\'' @ C @ D ) ) )
       => ( ( '\'const/realax/real_le\'' @ A @ ( '\'const/sets/inf\'' @ B ) )
          = ( ! [C: '\'type/realax/real\''] :
                ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ B )
               => ( '\'const/realax/real_le\'' @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(6,plain,
    ( ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) )
   != ( ! [A: '\'type/realax/real\''] :
          ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ sk2 )
         => ( '\'const/realax/real_le\'' @ sk1 @ A ) ) ) ),
    inference(cnf,[status(esa)],[5]) ).

thf(9,plain,
    ( ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) )
   != ( ! [A: '\'type/realax/real\''] :
          ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ sk2 )
         => ( '\'const/realax/real_le\'' @ sk1 @ A ) ) ) ),
    inference(lifteq,[status(thm)],[6]) ).

thf(28,plain,
    ( ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) )
    | ! [A: '\'type/realax/real\''] :
        ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ sk2 )
       => ( '\'const/realax/real_le\'' @ sk1 @ A ) ) ),
    inference(bool_ext,[status(thm)],[9]) ).

thf(31,plain,
    ! [A: '\'type/realax/real\''] :
      ( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ sk2 )
      | ( '\'const/realax/real_le\'' @ sk1 @ A )
      | ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) ) ),
    inference(cnf,[status(esa)],[28]) ).

thf(4,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(13,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)],[4]) ).

thf(16,plain,
    ! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
      ( ( A
        = ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
      | ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk5 @ B @ A ) @ A )
      | ( sk4 @ A ) ),
    inference(cnf,[status(esa)],[13]) ).

thf(22,plain,
    ! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
      ( ( A
        = ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
      | ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk5 @ B @ A ) @ A )
      | ( sk4 @ A ) ),
    inference(lifteq,[status(thm)],[16]) ).

thf(8,plain,
    ( sk2
   != ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) ),
    inference(cnf,[status(esa)],[5]) ).

thf(10,plain,
    ( sk2
   != ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) ),
    inference(lifteq,[status(thm)],[8]) ).

thf(141,plain,
    ! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
      ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk5 @ B @ A ) @ A )
      | ( sk4 @ A )
      | ( A != sk2 ) ),
    inference(paramod_ordered,[status(thm)],[22,10]) ).

thf(142,plain,
    ! [A: '\'type/realax/real\''] :
      ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk5 @ A @ sk2 ) @ sk2 )
      | ( sk4 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[141:[bind(A,$thf( sk2 )),bind(B,$thf( B ))]]) ).

thf(164,plain,
    ! [A: '\'type/realax/real\''] :
      ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk5 @ A @ sk2 ) @ sk2 )
      | ( sk4 @ sk2 ) ),
    inference(simp,[status(thm)],[142]) ).

thf(7,plain,
    ! [A: '\'type/realax/real\''] :
      ( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ sk2 )
      | ( '\'const/realax/real_le\'' @ sk3 @ A ) ),
    inference(cnf,[status(esa)],[5]) ).

thf(183,plain,
    ! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
      ( ( sk4 @ sk2 )
      | ( '\'const/realax/real_le\'' @ sk3 @ B )
      | ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk5 @ A @ sk2 ) @ sk2 )
       != ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ B @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[164,7]) ).

thf(184,plain,
    ! [A: '\'type/realax/real\''] :
      ( ( sk4 @ sk2 )
      | ( '\'const/realax/real_le\'' @ sk3 @ ( sk5 @ A @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[183:[bind(A,$thf( C )),bind(B,$thf( sk5 @ C @ sk2 ))]]) ).

thf(194,plain,
    ! [A: '\'type/realax/real\''] :
      ( ( sk4 @ sk2 )
      | ( '\'const/realax/real_le\'' @ sk3 @ ( sk5 @ A @ sk2 ) ) ),
    inference(simp,[status(thm)],[184]) ).

thf(17,plain,
    ! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
      ( ( A
        = ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
      | ~ ( '\'const/realax/real_le\'' @ B @ ( sk5 @ B @ A ) )
      | ( sk4 @ A ) ),
    inference(cnf,[status(esa)],[13]) ).

thf(20,plain,
    ! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
      ( ( A
        = ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
      | ~ ( '\'const/realax/real_le\'' @ B @ ( sk5 @ B @ A ) )
      | ( sk4 @ A ) ),
    inference(lifteq,[status(thm)],[17]) ).

thf(573,plain,
    ! [C: '\'type/realax/real\'',B: '\'type/realax/real\'' > $o,A: '\'type/realax/real\''] :
      ( ( sk4 @ sk2 )
      | ( B
        = ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
      | ( sk4 @ B )
      | ( ( '\'const/realax/real_le\'' @ sk3 @ ( sk5 @ A @ sk2 ) )
       != ( '\'const/realax/real_le\'' @ C @ ( sk5 @ C @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[194,20]) ).

thf(574,plain,
    ( ( sk4 @ sk2 )
    | ( sk2
      = ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
    | ( sk4 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[573:[bind(A,$thf( sk3 )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).

thf(624,plain,
    ( ( sk4 @ sk2 )
    | ( sk2
      = ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) ) ),
    inference(simp,[status(thm)],[574]) ).

thf(625,plain,
    sk4 @ sk2,
    inference(simplifyReflect,[status(thm)],[624,10]) ).

thf(15,plain,
    ! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
      ( ~ ( sk4 @ A )
      | ~ ( '\'const/realax/real_le\'' @ B @ ( sk6 @ B @ A ) )
      | ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) ) ),
    inference(cnf,[status(esa)],[13]) ).

thf(23,plain,
    ! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
      ( ~ ( sk4 @ A )
      | ~ ( '\'const/realax/real_le\'' @ B @ ( sk6 @ B @ A ) )
      | ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) ) ),
    inference(simp,[status(thm)],[15]) ).

thf(1373,plain,
    ! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
      ( ~ ( '\'const/realax/real_le\'' @ B @ ( sk6 @ B @ A ) )
      | ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) )
      | ( ( sk4 @ sk2 )
       != ( sk4 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[625,23]) ).

thf(1374,plain,
    ! [A: '\'type/realax/real\''] :
      ( ~ ( '\'const/realax/real_le\'' @ A @ ( sk6 @ A @ sk2 ) )
      | ( '\'const/realax/real_le\'' @ A @ ( '\'const/sets/inf\'' @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[1373:[bind(A,$thf( sk2 )),bind(B,$thf( B ))]]) ).

thf(1411,plain,
    ! [A: '\'type/realax/real\''] :
      ( ~ ( '\'const/realax/real_le\'' @ A @ ( sk6 @ A @ sk2 ) )
      | ( '\'const/realax/real_le\'' @ A @ ( '\'const/sets/inf\'' @ sk2 ) ) ),
    inference(simp,[status(thm)],[1374]) ).

thf(53407,plain,
    ! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
      ( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ sk2 )
      | ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) )
      | ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ sk2 ) )
      | ( ( '\'const/realax/real_le\'' @ sk1 @ A )
       != ( '\'const/realax/real_le\'' @ B @ ( sk6 @ B @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[31,1411]) ).

thf(53408,plain,
    ( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ sk1 @ sk2 ) @ sk2 )
    | ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) )
    | ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[53407:[bind(A,$thf( sk6 @ sk1 @ sk2 )),bind(B,$thf( sk1 ))]]) ).

thf(53529,plain,
    ( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ sk1 @ sk2 ) @ sk2 )
    | ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) ) ),
    inference(simp,[status(thm)],[53408]) ).

thf(18,plain,
    ! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
      ( ~ ( sk4 @ A )
      | ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ B @ A )
      | ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ A ) @ B ) ),
    inference(cnf,[status(esa)],[13]) ).

thf(21,plain,
    ! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
      ( ~ ( sk4 @ A )
      | ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ B @ A )
      | ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ A ) @ B ) ),
    inference(simp,[status(thm)],[18]) ).

thf(890,plain,
    ! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
      ( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ B @ A )
      | ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ A ) @ B )
      | ( ( sk4 @ sk2 )
       != ( sk4 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[625,21]) ).

thf(891,plain,
    ! [A: '\'type/realax/real\''] :
      ( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ sk2 )
      | ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ sk2 ) @ A ) ),
    inference(pattern_uni,[status(thm)],[890:[bind(A,$thf( sk2 )),bind(B,$thf( B ))]]) ).

thf(958,plain,
    ! [A: '\'type/realax/real\''] :
      ( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ sk2 )
      | ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ sk2 ) @ A ) ),
    inference(simp,[status(thm)],[891]) ).

thf(3,axiom,
    ! [A: '\'type/realax/real\'',B: '\'type/realax/real\'',C: '\'type/realax/real\''] :
      ( ( ( '\'const/realax/real_le\'' @ A @ B )
        & ( '\'const/realax/real_le\'' @ B @ C ) )
     => ( '\'const/realax/real_le\'' @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/realax/REAL_LE_TRANS_') ).

thf(11,plain,
    ! [A: '\'type/realax/real\'',B: '\'type/realax/real\'',C: '\'type/realax/real\''] :
      ( ( ( '\'const/realax/real_le\'' @ A @ B )
        & ( '\'const/realax/real_le\'' @ B @ C ) )
     => ( '\'const/realax/real_le\'' @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(12,plain,
    ! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
      ( ~ ( '\'const/realax/real_le\'' @ A @ B )
      | ~ ( '\'const/realax/real_le\'' @ B @ C )
      | ( '\'const/realax/real_le\'' @ A @ C ) ),
    inference(cnf,[status(esa)],[11]) ).

thf(27,plain,
    ( ~ ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) )
    | ~ ! [A: '\'type/realax/real\''] :
          ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ sk2 )
         => ( '\'const/realax/real_le\'' @ sk1 @ A ) ) ),
    inference(bool_ext,[status(thm)],[9]) ).

thf(29,plain,
    ( ~ ( '\'const/realax/real_le\'' @ sk1 @ sk8 )
    | ~ ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) ) ),
    inference(cnf,[status(esa)],[27]) ).

thf(58,plain,
    ! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
      ( ~ ( '\'const/realax/real_le\'' @ A @ B )
      | ~ ( '\'const/realax/real_le\'' @ B @ C )
      | ~ ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) )
      | ( ( '\'const/realax/real_le\'' @ A @ C )
       != ( '\'const/realax/real_le\'' @ sk1 @ sk8 ) ) ),
    inference(paramod_ordered,[status(thm)],[12,29]) ).

thf(59,plain,
    ! [A: '\'type/realax/real\''] :
      ( ~ ( '\'const/realax/real_le\'' @ sk1 @ A )
      | ~ ( '\'const/realax/real_le\'' @ A @ sk8 )
      | ~ ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[58:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( sk8 ))]]) ).

thf(81,plain,
    ! [A: '\'type/realax/real\''] :
      ( ~ ( '\'const/realax/real_le\'' @ sk1 @ A )
      | ~ ( '\'const/realax/real_le\'' @ A @ sk8 )
      | ~ ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) ) ),
    inference(simp,[status(thm)],[59]) ).

thf(5433,plain,
    ! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
      ( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ sk2 )
      | ~ ( '\'const/realax/real_le\'' @ sk1 @ B )
      | ~ ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) )
      | ( ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ sk2 ) @ A )
       != ( '\'const/realax/real_le\'' @ B @ sk8 ) ) ),
    inference(paramod_ordered,[status(thm)],[958,81]) ).

thf(5434,plain,
    ( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk8 @ sk2 )
    | ~ ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) )
    | ~ ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[5433:[bind(A,$thf( sk8 )),bind(B,$thf( '\'const/sets/inf\'' @ sk2 ))]]) ).

thf(5617,plain,
    ( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk8 @ sk2 )
    | ~ ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) ) ),
    inference(simp,[status(thm)],[5434]) ).

thf(14,plain,
    ! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
      ( ~ ( sk4 @ A )
      | ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ B @ A ) @ A )
      | ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) ) ),
    inference(cnf,[status(esa)],[13]) ).

thf(19,plain,
    ! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
      ( ~ ( sk4 @ A )
      | ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ B @ A ) @ A )
      | ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) ) ),
    inference(simp,[status(thm)],[14]) ).

thf(30,plain,
    ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk8 @ sk2 )
    | ~ ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) ) ),
    inference(cnf,[status(esa)],[27]) ).

thf(255,plain,
    ! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
      ( ~ ( sk4 @ A )
      | ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ B @ A ) @ A )
      | ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk8 @ sk2 )
      | ( ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) )
       != ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[19,30]) ).

thf(256,plain,
    ( ~ ( sk4 @ sk2 )
    | ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ sk1 @ sk2 ) @ sk2 )
    | ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk8 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[255:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 ))]]) ).

thf(626,plain,
    ( ~ $true
    | ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ sk1 @ sk2 ) @ sk2 )
    | ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk8 @ sk2 ) ),
    inference(rewrite,[status(thm)],[256,625]) ).

thf(627,plain,
    ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ sk1 @ sk2 ) @ sk2 )
    | ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk8 @ sk2 ) ),
    inference(simp,[status(thm)],[626]) ).

thf(1985,plain,
    ! [A: '\'type/realax/real\''] :
      ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk8 @ sk2 )
      | ( '\'const/realax/real_le\'' @ sk1 @ A )
      | ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) )
      | ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ sk1 @ sk2 ) @ sk2 )
       != ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[627,31]) ).

thf(1986,plain,
    ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk8 @ sk2 )
    | ( '\'const/realax/real_le\'' @ sk1 @ ( sk6 @ sk1 @ sk2 ) )
    | ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[1985:[bind(A,$thf( sk6 @ sk1 @ sk2 ))]]) ).

thf(53423,plain,
    ! [A: '\'type/realax/real\''] :
      ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk8 @ sk2 )
      | ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) )
      | ( '\'const/realax/real_le\'' @ A @ ( '\'const/sets/inf\'' @ sk2 ) )
      | ( ( '\'const/realax/real_le\'' @ sk1 @ ( sk6 @ sk1 @ sk2 ) )
       != ( '\'const/realax/real_le\'' @ A @ ( sk6 @ A @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1986,1411]) ).

thf(53424,plain,
    ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk8 @ sk2 )
    | ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) )
    | ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[53423:[bind(A,$thf( sk1 ))]]) ).

thf(53531,plain,
    ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk8 @ sk2 )
    | ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) ) ),
    inference(simp,[status(thm)],[53424]) ).

thf(53780,plain,
    ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk8 @ sk2 )
    | ( ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) )
     != ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[53531,30]) ).

thf(53781,plain,
    '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk8 @ sk2,
    inference(pattern_uni,[status(thm)],[53780:[]]) ).

thf(54095,plain,
    ( ~ $true
    | ~ ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) ) ),
    inference(rewrite,[status(thm)],[5617,53781]) ).

thf(54096,plain,
    ~ ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) ),
    inference(simp,[status(thm)],[54095]) ).

thf(634,plain,
    ! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
      ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ B @ A ) @ A )
      | ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) )
      | ( ( sk4 @ sk2 )
       != ( sk4 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[625,19]) ).

thf(635,plain,
    ! [A: '\'type/realax/real\''] :
      ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ A @ sk2 ) @ sk2 )
      | ( '\'const/realax/real_le\'' @ A @ ( '\'const/sets/inf\'' @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[634:[bind(A,$thf( sk2 )),bind(B,$thf( B ))]]) ).

thf(638,plain,
    ! [A: '\'type/realax/real\''] :
      ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ A @ sk2 ) @ sk2 )
      | ( '\'const/realax/real_le\'' @ A @ ( '\'const/sets/inf\'' @ sk2 ) ) ),
    inference(simp,[status(thm)],[635]) ).

thf(5639,plain,
    ! [A: '\'type/realax/real\''] :
      ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ A @ sk2 ) @ sk2 )
      | ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk8 @ sk2 )
      | ( ( '\'const/realax/real_le\'' @ A @ ( '\'const/sets/inf\'' @ sk2 ) )
       != ( '\'const/realax/real_le\'' @ sk1 @ ( '\'const/sets/inf\'' @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[638,5617]) ).

thf(5640,plain,
    ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ sk1 @ sk2 ) @ sk2 )
    | ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ sk8 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[5639:[bind(A,$thf( sk1 ))]]) ).

thf(54093,plain,
    ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ sk1 @ sk2 ) @ sk2 )
    | ~ $true ),
    inference(rewrite,[status(thm)],[5640,53781]) ).

thf(54094,plain,
    '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk6 @ sk1 @ sk2 ) @ sk2,
    inference(simp,[status(thm)],[54093]) ).

thf(60307,plain,
    ( ~ $true
    | $false ),
    inference(rewrite,[status(thm)],[53529,54096,54094]) ).

thf(60308,plain,
    $false,
    inference(simp,[status(thm)],[60307]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.09  % Problem  : ANA092^1 : TPTP v8.2.0. Released v7.0.0.
% 0.03/0.11  % Command  : run_Leo-III %s %d
% 0.10/0.31  % Computer : n016.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Mon May 20 07:58:24 EDT 2024
% 0.10/0.32  % CPUTime  : 
% 0.94/0.92  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.31/1.09  % [INFO] 	 Parsing done (172ms). 
% 1.31/1.10  % [INFO] 	 Running in sequential loop mode. 
% 1.74/1.45  % [INFO] 	 nitpick registered as external prover. 
% 1.74/1.45  % [INFO] 	 Scanning for conjecture ... 
% 2.02/1.55  % [INFO] 	 Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ... 
% 2.02/1.59  % [INFO] 	 Axiom selection finished. Selected 2 axioms (removed 0 axioms). 
% 2.02/1.60  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.02/1.61  % [INFO] 	 Type checking passed. 
% 2.02/1.61  % [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 ... 
% 135.32/22.39  % [INFO] 	 Killing All external provers ... 
% 135.32/22.40  % Time passed: 21933ms (effective reasoning time: 21286ms)
% 135.32/22.40  % 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)>
% 135.32/22.40  % Axioms used in derivation (2): thm/sets/INF_, thm/realax/REAL_LE_TRANS_
% 135.32/22.40  % No. of inferences in proof: 75
% 135.32/22.40  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 21933 ms resp. 21286 ms w/o parsing
% 135.32/22.46  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 135.32/22.46  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------