TSTP Solution File: ANA101^1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : ANA101^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n005.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 18:39:45 EDT 2024

% Result   : Theorem 13.01s 3.27s
% Output   : Refutation 13.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   45 (  13 unt;  10 typ;   0 def)
%            Number of atoms       :  110 (  52 equ;   0 cnn)
%            Maximal formula atoms :    4 (   3 avg)
%            Number of connectives :  577 (  45   ~;  28   |;   0   &; 499   @)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   67 (  67   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8 usr;   2 con; 0-3 aty)
%            Number of variables   :  131 (  46   ^  83   !;   0   ?; 131   :)
%                                         (   2  !>;   0  ?*;   0  @-;   0  @+)

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

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

thf('\'const/realax/real_sub\'_type',type,
    '\'const/realax/real_sub\'': '\'type/realax/real\'' > '\'type/realax/real\'' > '\'type/realax/real\'' ).

thf('\'const/realax/real_neg\'_type',type,
    '\'const/realax/real_neg\'': '\'type/realax/real\'' > '\'type/realax/real\'' ).

thf('\'const/realax/real_add\'_type',type,
    '\'const/realax/real_add\'': '\'type/realax/real\'' > '\'type/realax/real\'' > '\'type/realax/real\'' ).

thf('\'const/iterate/sum\'_type',type,
    '\'const/iterate/sum\'': 
      !>[TA: $tType] : ( ( TA > $o ) > ( TA > '\'type/realax/real\'' ) > '\'type/realax/real\'' ) ).

thf(skt1_type,type,
    skt1: $tType ).

thf(sk1_type,type,
    sk1: skt1 > '\'type/realax/real\'' ).

thf(sk2_type,type,
    sk2: skt1 > '\'type/realax/real\'' ).

thf(sk3_type,type,
    sk3: skt1 > $o ).

thf(3,axiom,
    ! [TA: $tType,A: TA > '\'type/realax/real\'',B: TA > $o] :
      ( ( '\'const/iterate/sum\'' @ TA @ B
        @ ^ [C: TA] : ( '\'const/realax/real_neg\'' @ ( A @ C ) ) )
      = ( '\'const/realax/real_neg\'' @ ( '\'const/iterate/sum\'' @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_NEG_') ).

thf(10,plain,
    ! [TA: $tType,A: TA > '\'type/realax/real\'',B: TA > $o] :
      ( ( '\'const/iterate/sum\'' @ TA @ B
        @ ^ [C: TA] : ( '\'const/realax/real_neg\'' @ ( A @ C ) ) )
      = ( '\'const/realax/real_neg\'' @ ( '\'const/iterate/sum\'' @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(11,plain,
    ! [TA: $tType,B: TA > $o,A: TA > '\'type/realax/real\''] :
      ( ( '\'const/iterate/sum\'' @ TA @ B
        @ ^ [C: TA] : ( '\'const/realax/real_neg\'' @ ( A @ C ) ) )
      = ( '\'const/realax/real_neg\'' @ ( '\'const/iterate/sum\'' @ TA @ B @ A ) ) ),
    inference(cnf,[status(esa)],[10]) ).

thf(12,plain,
    ! [TA: $tType,B: TA > $o,A: TA > '\'type/realax/real\''] :
      ( ( '\'const/iterate/sum\'' @ TA @ B
        @ ^ [C: TA] : ( '\'const/realax/real_neg\'' @ ( A @ C ) ) )
      = ( '\'const/realax/real_neg\'' @ ( '\'const/iterate/sum\'' @ TA @ B @ A ) ) ),
    inference(lifteq,[status(thm)],[11]) ).

thf(5,axiom,
    ! [A: '\'type/realax/real\'',B: '\'type/realax/real\''] :
      ( ( '\'const/realax/real_sub\'' @ A @ B )
      = ( '\'const/realax/real_add\'' @ A @ ( '\'const/realax/real_neg\'' @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/realax/real_sub_') ).

thf(16,plain,
    ! [A: '\'type/realax/real\'',B: '\'type/realax/real\''] :
      ( ( '\'const/realax/real_sub\'' @ A @ B )
      = ( '\'const/realax/real_add\'' @ A @ ( '\'const/realax/real_neg\'' @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(17,plain,
    ! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
      ( ( '\'const/realax/real_sub\'' @ A @ B )
      = ( '\'const/realax/real_add\'' @ A @ ( '\'const/realax/real_neg\'' @ B ) ) ),
    inference(cnf,[status(esa)],[16]) ).

thf(18,plain,
    ! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
      ( ( '\'const/realax/real_add\'' @ A @ ( '\'const/realax/real_neg\'' @ B ) )
      = ( '\'const/realax/real_sub\'' @ A @ B ) ),
    inference(lifteq,[status(thm)],[17]) ).

thf(4,axiom,
    ! [TA: $tType,A: TA > '\'type/realax/real\'',B: TA > '\'type/realax/real\'',C: TA > $o] :
      ( ( '\'const/sets/FINITE\'' @ TA @ C )
     => ( ( '\'const/iterate/sum\'' @ TA @ C
          @ ^ [D: TA] : ( '\'const/realax/real_add\'' @ ( A @ D ) @ ( B @ D ) ) )
        = ( '\'const/realax/real_add\'' @ ( '\'const/iterate/sum\'' @ TA @ C @ A ) @ ( '\'const/iterate/sum\'' @ TA @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_ADD_') ).

thf(13,plain,
    ! [TA: $tType,A: TA > '\'type/realax/real\'',B: TA > '\'type/realax/real\'',C: TA > $o] :
      ( ( '\'const/sets/FINITE\'' @ TA @ C )
     => ( ( '\'const/iterate/sum\'' @ TA @ C
          @ ^ [D: TA] : ( '\'const/realax/real_add\'' @ ( A @ D ) @ ( B @ D ) ) )
        = ( '\'const/realax/real_add\'' @ ( '\'const/iterate/sum\'' @ TA @ C @ A ) @ ( '\'const/iterate/sum\'' @ TA @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(14,plain,
    ! [TA: $tType,C: TA > $o,B: TA > '\'type/realax/real\'',A: TA > '\'type/realax/real\''] :
      ( ~ ( '\'const/sets/FINITE\'' @ TA @ C )
      | ( ( '\'const/iterate/sum\'' @ TA @ C
          @ ^ [D: TA] : ( '\'const/realax/real_add\'' @ ( A @ D ) @ ( B @ D ) ) )
        = ( '\'const/realax/real_add\'' @ ( '\'const/iterate/sum\'' @ TA @ C @ A ) @ ( '\'const/iterate/sum\'' @ TA @ C @ B ) ) ) ),
    inference(cnf,[status(esa)],[13]) ).

thf(15,plain,
    ! [TA: $tType,C: TA > $o,B: TA > '\'type/realax/real\'',A: TA > '\'type/realax/real\''] :
      ( ( ( '\'const/iterate/sum\'' @ TA @ C
          @ ^ [D: TA] : ( '\'const/realax/real_add\'' @ ( A @ D ) @ ( B @ D ) ) )
        = ( '\'const/realax/real_add\'' @ ( '\'const/iterate/sum\'' @ TA @ C @ A ) @ ( '\'const/iterate/sum\'' @ TA @ C @ B ) ) )
      | ~ ( '\'const/sets/FINITE\'' @ TA @ C ) ),
    inference(lifteq,[status(thm)],[14]) ).

thf(40,plain,
    ! [TA: $tType,E: TA > $o,D: TA > '\'type/realax/real\'',C: TA > '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
      ( ( ( '\'const/realax/real_sub\'' @ A @ B )
        = ( '\'const/iterate/sum\'' @ TA @ E
          @ ^ [F: TA] : ( '\'const/realax/real_add\'' @ ( C @ F ) @ ( D @ F ) ) ) )
      | ~ ( '\'const/sets/FINITE\'' @ TA @ E )
      | ( ( '\'const/realax/real_add\'' @ A @ ( '\'const/realax/real_neg\'' @ B ) )
       != ( '\'const/realax/real_add\'' @ ( '\'const/iterate/sum\'' @ TA @ E @ C ) @ ( '\'const/iterate/sum\'' @ TA @ E @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[18,15]) ).

thf(48,plain,
    ! [TA: $tType,E: TA > $o,D: TA > '\'type/realax/real\'',C: TA > '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
      ( ( ( '\'const/realax/real_sub\'' @ A @ B )
        = ( '\'const/iterate/sum\'' @ TA @ E
          @ ^ [F: TA] : ( '\'const/realax/real_add\'' @ ( C @ F ) @ ( D @ F ) ) ) )
      | ~ ( '\'const/sets/FINITE\'' @ TA @ E )
      | ( A
       != ( '\'const/iterate/sum\'' @ TA @ E @ C ) )
      | ( ( '\'const/realax/real_neg\'' @ B )
       != ( '\'const/iterate/sum\'' @ TA @ E @ D ) ) ),
    inference(simp,[status(thm)],[40]) ).

thf(49,plain,
    ! [TA: $tType,D: TA > $o,C: TA > '\'type/realax/real\'',B: TA > '\'type/realax/real\'',A: '\'type/realax/real\''] :
      ( ( ( '\'const/realax/real_sub\'' @ ( '\'const/iterate/sum\'' @ TA @ D @ B ) @ A )
        = ( '\'const/iterate/sum\'' @ TA @ D
          @ ^ [E: TA] : ( '\'const/realax/real_add\'' @ ( B @ E ) @ ( C @ E ) ) ) )
      | ~ ( '\'const/sets/FINITE\'' @ TA @ D )
      | ( ( '\'const/realax/real_neg\'' @ A )
       != ( '\'const/iterate/sum\'' @ TA @ D @ C ) ) ),
    inference(simp,[status(thm)],[48]) ).

thf(1,conjecture,
    ! [TA: $tType,A: TA > '\'type/realax/real\'',B: TA > '\'type/realax/real\'',C: TA > $o] :
      ( ( '\'const/sets/FINITE\'' @ TA @ C )
     => ( ( '\'const/iterate/sum\'' @ TA @ C
          @ ^ [D: TA] : ( '\'const/realax/real_sub\'' @ ( A @ D ) @ ( B @ D ) ) )
        = ( '\'const/realax/real_sub\'' @ ( '\'const/iterate/sum\'' @ TA @ C @ A ) @ ( '\'const/iterate/sum\'' @ TA @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_SUB_') ).

thf(2,negated_conjecture,
    ~ ! [TA: $tType,A: TA > '\'type/realax/real\'',B: TA > '\'type/realax/real\'',C: TA > $o] :
        ( ( '\'const/sets/FINITE\'' @ TA @ C )
       => ( ( '\'const/iterate/sum\'' @ TA @ C
            @ ^ [D: TA] : ( '\'const/realax/real_sub\'' @ ( A @ D ) @ ( B @ D ) ) )
          = ( '\'const/realax/real_sub\'' @ ( '\'const/iterate/sum\'' @ TA @ C @ A ) @ ( '\'const/iterate/sum\'' @ TA @ C @ B ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(6,plain,
    ~ ! [TA: $tType,A: TA > '\'type/realax/real\'',B: TA > '\'type/realax/real\'',C: TA > $o] :
        ( ( '\'const/sets/FINITE\'' @ TA @ C )
       => ( ( '\'const/iterate/sum\'' @ TA @ C
            @ ^ [D: TA] : ( '\'const/realax/real_sub\'' @ ( A @ D ) @ ( B @ D ) ) )
          = ( '\'const/realax/real_sub\'' @ ( '\'const/iterate/sum\'' @ TA @ C @ A ) @ ( '\'const/iterate/sum\'' @ TA @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(7,plain,
    ( ( '\'const/iterate/sum\'' @ skt1 @ sk3
      @ ^ [A: skt1] : ( '\'const/realax/real_sub\'' @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
   != ( '\'const/realax/real_sub\'' @ ( '\'const/iterate/sum\'' @ skt1 @ sk3 @ sk1 ) @ ( '\'const/iterate/sum\'' @ skt1 @ sk3 @ sk2 ) ) ),
    inference(cnf,[status(esa)],[6]) ).

thf(9,plain,
    ( ( '\'const/iterate/sum\'' @ skt1 @ sk3
      @ ^ [A: skt1] : ( '\'const/realax/real_sub\'' @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
   != ( '\'const/realax/real_sub\'' @ ( '\'const/iterate/sum\'' @ skt1 @ sk3 @ sk1 ) @ ( '\'const/iterate/sum\'' @ skt1 @ sk3 @ sk2 ) ) ),
    inference(lifteq,[status(thm)],[7]) ).

thf(56,plain,
    ! [TA: $tType,D: TA > $o,C: TA > '\'type/realax/real\'',B: TA > '\'type/realax/real\'',A: '\'type/realax/real\''] :
      ( ~ ( '\'const/sets/FINITE\'' @ TA @ D )
      | ( ( '\'const/realax/real_neg\'' @ A )
       != ( '\'const/iterate/sum\'' @ TA @ D @ C ) )
      | ( ( '\'const/iterate/sum\'' @ TA @ D
          @ ^ [E: TA] : ( '\'const/realax/real_add\'' @ ( B @ E ) @ ( C @ E ) ) )
       != ( '\'const/iterate/sum\'' @ skt1 @ sk3
          @ ^ [E: skt1] : ( '\'const/realax/real_sub\'' @ ( sk1 @ E ) @ ( sk2 @ E ) ) ) )
      | ( ( '\'const/realax/real_sub\'' @ ( '\'const/iterate/sum\'' @ TA @ D @ B ) @ A )
       != ( '\'const/realax/real_sub\'' @ ( '\'const/iterate/sum\'' @ skt1 @ sk3 @ sk1 ) @ ( '\'const/iterate/sum\'' @ skt1 @ sk3 @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[49,9]) ).

thf(57,plain,
    ! [A: skt1 > '\'type/realax/real\''] :
      ( ~ ( '\'const/sets/FINITE\'' @ skt1 @ sk3 )
      | ( ( '\'const/realax/real_neg\'' @ ( '\'const/iterate/sum\'' @ skt1 @ sk3 @ sk2 ) )
       != ( '\'const/iterate/sum\'' @ skt1 @ sk3 @ A ) )
      | ( ( '\'const/iterate/sum\'' @ skt1 @ sk3
          @ ^ [B: skt1] : ( '\'const/realax/real_add\'' @ ( sk1 @ B ) @ ( A @ B ) ) )
       != ( '\'const/iterate/sum\'' @ skt1 @ sk3
          @ ^ [B: skt1] : ( '\'const/realax/real_sub\'' @ ( sk1 @ B ) @ ( sk2 @ B ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[56:[bind(A,$thf( '\'const/iterate/sum\'' @ skt1 @ sk3 @ sk2 )),bind(B,$thf( sk1 )),bind(C,$thf( C )),bind(D,$thf( sk3 )),bind_type(TA,$thf( skt1 ))]]) ).

thf(102,plain,
    ! [A: skt1 > '\'type/realax/real\''] :
      ( ~ ( '\'const/sets/FINITE\'' @ skt1 @ sk3 )
      | ( ( '\'const/realax/real_neg\'' @ ( '\'const/iterate/sum\'' @ skt1 @ sk3 @ sk2 ) )
       != ( '\'const/iterate/sum\'' @ skt1 @ sk3 @ A ) )
      | ( ( '\'const/iterate/sum\'' @ skt1 @ sk3
          @ ^ [B: skt1] : ( '\'const/realax/real_add\'' @ ( sk1 @ B ) @ ( A @ B ) ) )
       != ( '\'const/iterate/sum\'' @ skt1 @ sk3
          @ ^ [B: skt1] : ( '\'const/realax/real_sub\'' @ ( sk1 @ B ) @ ( sk2 @ B ) ) ) ) ),
    inference(simp,[status(thm)],[57]) ).

thf(8,plain,
    '\'const/sets/FINITE\'' @ skt1 @ sk3,
    inference(cnf,[status(esa)],[6]) ).

thf(694,plain,
    ! [A: skt1 > '\'type/realax/real\''] :
      ( ~ $true
      | ( ( '\'const/realax/real_neg\'' @ ( '\'const/iterate/sum\'' @ skt1 @ sk3 @ sk2 ) )
       != ( '\'const/iterate/sum\'' @ skt1 @ sk3 @ A ) )
      | ( ( '\'const/iterate/sum\'' @ skt1 @ sk3
          @ ^ [B: skt1] : ( '\'const/realax/real_add\'' @ ( sk1 @ B ) @ ( A @ B ) ) )
       != ( '\'const/iterate/sum\'' @ skt1 @ sk3
          @ ^ [B: skt1] : ( '\'const/realax/real_sub\'' @ ( sk1 @ B ) @ ( sk2 @ B ) ) ) ) ),
    inference(rewrite,[status(thm)],[102,8]) ).

thf(695,plain,
    ! [A: skt1 > '\'type/realax/real\''] :
      ( ( ( '\'const/realax/real_neg\'' @ ( '\'const/iterate/sum\'' @ skt1 @ sk3 @ sk2 ) )
       != ( '\'const/iterate/sum\'' @ skt1 @ sk3 @ A ) )
      | ( ( '\'const/iterate/sum\'' @ skt1 @ sk3
          @ ^ [B: skt1] : ( '\'const/realax/real_add\'' @ ( sk1 @ B ) @ ( A @ B ) ) )
       != ( '\'const/iterate/sum\'' @ skt1 @ sk3
          @ ^ [B: skt1] : ( '\'const/realax/real_sub\'' @ ( sk1 @ B ) @ ( sk2 @ B ) ) ) ) ),
    inference(simp,[status(thm)],[694]) ).

thf(696,plain,
    ! [A: skt1 > '\'type/realax/real\''] :
      ( ( ( '\'const/realax/real_neg\'' @ ( '\'const/iterate/sum\'' @ skt1 @ sk3 @ sk2 ) )
       != ( '\'const/iterate/sum\'' @ skt1 @ sk3 @ A ) )
      | ( sk3 != sk3 )
      | ( ( ^ [B: skt1] : ( '\'const/realax/real_add\'' @ ( sk1 @ B ) @ ( A @ B ) ) )
       != ( ^ [B: skt1] : ( '\'const/realax/real_sub\'' @ ( sk1 @ B ) @ ( sk2 @ B ) ) ) ) ),
    inference(simp,[status(thm)],[695]) ).

thf(781,plain,
    ! [A: skt1 > '\'type/realax/real\''] :
      ( ( ( '\'const/realax/real_neg\'' @ ( '\'const/iterate/sum\'' @ skt1 @ sk3 @ sk2 ) )
       != ( '\'const/iterate/sum\'' @ skt1 @ sk3 @ A ) )
      | ( ( ^ [B: skt1] : ( '\'const/realax/real_add\'' @ ( sk1 @ B ) @ ( A @ B ) ) )
       != ( ^ [B: skt1] : ( '\'const/realax/real_sub\'' @ ( sk1 @ B ) @ ( sk2 @ B ) ) ) ) ),
    inference(simp,[status(thm)],[696]) ).

thf(845,plain,
    ! [TA: $tType,C: skt1 > '\'type/realax/real\'',B: TA > $o,A: TA > '\'type/realax/real\''] :
      ( ( ( '\'const/iterate/sum\'' @ TA @ B
          @ ^ [D: TA] : ( '\'const/realax/real_neg\'' @ ( A @ D ) ) )
       != ( '\'const/iterate/sum\'' @ skt1 @ sk3 @ C ) )
      | ( ( ^ [D: skt1] : ( '\'const/realax/real_add\'' @ ( sk1 @ D ) @ ( C @ D ) ) )
       != ( ^ [D: skt1] : ( '\'const/realax/real_sub\'' @ ( sk1 @ D ) @ ( sk2 @ D ) ) ) )
      | ( ( '\'const/realax/real_neg\'' @ ( '\'const/iterate/sum\'' @ TA @ B @ A ) )
       != ( '\'const/realax/real_neg\'' @ ( '\'const/iterate/sum\'' @ skt1 @ sk3 @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[12,781]) ).

thf(846,plain,
    ! [A: skt1 > '\'type/realax/real\''] :
      ( ( ( '\'const/iterate/sum\'' @ skt1 @ sk3
          @ ^ [B: skt1] : ( '\'const/realax/real_neg\'' @ ( sk2 @ B ) ) )
       != ( '\'const/iterate/sum\'' @ skt1 @ sk3 @ A ) )
      | ( ( ^ [B: skt1] : ( '\'const/realax/real_add\'' @ ( sk1 @ B ) @ ( A @ B ) ) )
       != ( ^ [B: skt1] : ( '\'const/realax/real_sub\'' @ ( sk1 @ B ) @ ( sk2 @ B ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[845:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 )),bind(C,$thf( C )),bind_type(TA,$thf( skt1 ))]]) ).

thf(864,plain,
    ! [A: skt1 > '\'type/realax/real\''] :
      ( ( ( '\'const/iterate/sum\'' @ skt1 @ sk3
          @ ^ [B: skt1] : ( '\'const/realax/real_neg\'' @ ( sk2 @ B ) ) )
       != ( '\'const/iterate/sum\'' @ skt1 @ sk3 @ A ) )
      | ( ( ^ [B: skt1] : ( '\'const/realax/real_add\'' @ ( sk1 @ B ) @ ( A @ B ) ) )
       != ( ^ [B: skt1] : ( '\'const/realax/real_sub\'' @ ( sk1 @ B ) @ ( sk2 @ B ) ) ) ) ),
    inference(simp,[status(thm)],[846]) ).

thf(873,plain,
    ! [A: skt1 > '\'type/realax/real\''] :
      ( ( sk3 != sk3 )
      | ( ( ^ [B: skt1] : ( '\'const/realax/real_neg\'' @ ( sk2 @ B ) ) )
       != A )
      | ( ( ^ [B: skt1] : ( '\'const/realax/real_add\'' @ ( sk1 @ B ) @ ( A @ B ) ) )
       != ( ^ [B: skt1] : ( '\'const/realax/real_sub\'' @ ( sk1 @ B ) @ ( sk2 @ B ) ) ) ) ),
    inference(simp,[status(thm)],[864]) ).

thf(906,plain,
    ( ( ^ [A: skt1] : ( '\'const/realax/real_add\'' @ ( sk1 @ A ) @ ( '\'const/realax/real_neg\'' @ ( sk2 @ A ) ) ) )
   != ( ^ [A: skt1] : ( '\'const/realax/real_sub\'' @ ( sk1 @ A ) @ ( sk2 @ A ) ) ) ),
    inference(simp,[status(thm)],[873]) ).

thf(914,plain,
    ( ( ^ [A: skt1] : ( '\'const/realax/real_sub\'' @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
   != ( ^ [A: skt1] : ( '\'const/realax/real_sub\'' @ ( sk1 @ A ) @ ( sk2 @ A ) ) ) ),
    inference(rewrite,[status(thm)],[906,18]) ).

thf(915,plain,
    $false,
    inference(simp,[status(thm)],[914]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : ANA101^1 : TPTP v8.2.0. Released v7.0.0.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n005.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 07:42:24 EDT 2024
% 0.16/0.38  % CPUTime  : 
% 0.89/0.83  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.20/0.95  % [INFO] 	 Parsing done (109ms). 
% 1.20/0.95  % [INFO] 	 Running in sequential loop mode. 
% 1.55/1.15  % [INFO] 	 nitpick registered as external prover. 
% 1.64/1.16  % [INFO] 	 Scanning for conjecture ... 
% 1.64/1.21  % [INFO] 	 Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ... 
% 1.64/1.23  % [INFO] 	 Axiom selection finished. Selected 3 axioms (removed 0 axioms). 
% 1.87/1.24  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.87/1.25  % [INFO] 	 Type checking passed. 
% 1.87/1.25  % [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 ... 
% 13.01/3.26  % [INFO] 	 Killing All external provers ... 
% 13.01/3.26  % Time passed: 2746ms (effective reasoning time: 2304ms)
% 13.01/3.26  % 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)>
% 13.01/3.26  % Axioms used in derivation (3): thm/iterate/SUM_NEG_, thm/realax/real_sub_, thm/iterate/SUM_ADD_
% 13.01/3.26  % No. of inferences in proof: 35
% 13.01/3.27  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2746 ms resp. 2304 ms w/o parsing
% 13.23/3.38  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.23/3.38  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------