TSTP Solution File: NUM827^5 by Leo-III---1.7.10

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : NUM827^5 : TPTP v8.1.2. Bugfixed v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n002.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  7 08:00:57 EDT 2024

% Result   : Theorem 43.77s 9.55s
% Output   : Refutation 43.77s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   13
% Syntax   : Number of formulae    :  109 (  22 unt;   9 typ;   3 def)
%            Number of atoms       :  274 ( 264 equ;   0 cnn)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives : 1238 ( 213   ~; 153   |;   8   &; 857   @)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   57 (  57   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :  494 ( 379   ^ 115   !;   0   ?; 494   :)

% Comments : 
%------------------------------------------------------------------------------
thf(n_type,type,
    n: $tType ).

thf(c0_type,type,
    c0: n ).

thf(cS_type,type,
    cS: n > n ).

thf(c_plus_type,type,
    c_plus: n > n > n ).

thf(cPA_1_type,type,
    cPA_1: $o ).

thf(cPA_1_def,definition,
    ( cPA_1
    = ( ! [A: n] :
          ( ( c_plus @ A @ c0 )
          = A ) ) ) ).

thf(cPA_2_type,type,
    cPA_2: $o ).

thf(cPA_2_def,definition,
    ( cPA_2
    = ( ! [A: n,B: n] :
          ( ( c_plus @ A @ ( cS @ B ) )
          = ( cS @ ( c_plus @ A @ B ) ) ) ) ) ).

thf(cPA_IND_EQ_type,type,
    cPA_IND_EQ: $o ).

thf(cPA_IND_EQ_def,definition,
    ( cPA_IND_EQ
    = ( ! [A: n > n,B: n > n] :
          ( ( ( ( A @ c0 )
              = ( B @ c0 ) )
            & ! [C: n] :
                ( ( ( A @ C )
                  = ( B @ C ) )
               => ( ( A @ ( cS @ C ) )
                  = ( B @ ( cS @ C ) ) ) ) )
         => ! [C: n] :
              ( ( A @ C )
              = ( B @ C ) ) ) ) ) ).

thf(sk1_type,type,
    sk1: ( n > n ) > ( n > n ) > n ).

thf(sk2_type,type,
    sk2: n ).

thf(1,conjecture,
    ( ( cPA_1
      & cPA_2
      & cPA_IND_EQ )
   => ! [A: n] :
        ( ( c_plus @ A @ c0 )
        = ( c_plus @ c0 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cPA_THM2) ).

thf(2,negated_conjecture,
    ~ ( ( cPA_1
        & cPA_2
        & cPA_IND_EQ )
     => ! [A: n] :
          ( ( c_plus @ A @ c0 )
          = ( c_plus @ c0 @ A ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ( ! [A: n] :
            ( ( c_plus @ A @ c0 )
            = A )
        & ! [A: n,B: n] :
            ( ( c_plus @ A @ ( cS @ B ) )
            = ( cS @ ( c_plus @ A @ B ) ) )
        & ! [A: n > n,B: n > n] :
            ( ( ( ( A @ c0 )
                = ( B @ c0 ) )
              & ! [C: n] :
                  ( ( ( A @ C )
                    = ( B @ C ) )
                 => ( ( A @ ( cS @ C ) )
                    = ( B @ ( cS @ C ) ) ) ) )
           => ! [C: n] :
                ( ( A @ C )
                = ( B @ C ) ) ) )
     => ! [A: n] :
          ( ( c_plus @ A @ c0 )
          = ( c_plus @ c0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,plain,
    ! [C: n,B: n > n,A: n > n] :
      ( ( ( A @ c0 )
       != ( B @ c0 ) )
      | ( ( A @ ( sk1 @ B @ A ) )
        = ( B @ ( sk1 @ B @ A ) ) )
      | ( ( A @ C )
        = ( B @ C ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(15,plain,
    ! [C: n,B: n > n,A: n > n] :
      ( ( ( A @ c0 )
       != ( B @ c0 ) )
      | ( ( A @ ( sk1 @ B @ A ) )
        = ( B @ ( sk1 @ B @ A ) ) )
      | ( ( A @ C )
        = ( B @ C ) ) ),
    inference(lifteq,[status(thm)],[4]) ).

thf(16,plain,
    ! [C: n,B: n > n,A: n > n] :
      ( ( ( A @ c0 )
       != ( B @ c0 ) )
      | ( ( A @ ( sk1 @ B @ A ) )
        = ( B @ ( sk1 @ B @ A ) ) )
      | ( ( A @ C )
        = ( B @ C ) ) ),
    inference(simp,[status(thm)],[15]) ).

thf(5,plain,
    ( ( c_plus @ sk2 @ c0 )
   != ( c_plus @ c0 @ sk2 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(9,plain,
    ( ( c_plus @ sk2 @ c0 )
   != ( c_plus @ c0 @ sk2 ) ),
    inference(lifteq,[status(thm)],[5]) ).

thf(17,plain,
    ( ( sk2 != c0 )
    | ( sk2 != c0 ) ),
    inference(simp,[status(thm)],[9]) ).

thf(18,plain,
    sk2 != c0,
    inference(simp,[status(thm)],[17]) ).

thf(329,plain,
    ! [C: n,B: n > n,A: n > n] :
      ( ( ( A @ c0 )
       != ( B @ c0 ) )
      | ( ( A @ ( sk1 @ B @ A ) )
        = ( B @ ( sk1 @ B @ A ) ) )
      | ( ( A @ C )
       != c0 )
      | ( ( B @ C )
       != sk2 ) ),
    inference(paramod_ordered,[status(thm)],[16,18]) ).

thf(480,plain,
    ! [A: n > n] :
      ( ( ( A @ c0 )
       != c0 )
      | ( ( A
          @ ( sk1
            @ ^ [B: n] : B
            @ A ) )
        = ( sk1
          @ ^ [B: n] : B
          @ A ) )
      | ( ( A @ sk2 )
       != c0 ) ),
    inference(pre_uni,[status(thm)],[329:[bind(A,$thf( A )),bind(B,$thf( ^ [D: n] : D )),bind(C,$thf( sk2 ))]]) ).

thf(481,plain,
    ( ( sk1
      @ ^ [A: n] : A
      @ ^ [A: n] : c0 )
    = c0 ),
    inference(pre_uni,[status(thm)],[480:[bind(A,$thf( ^ [B: n] : c0 ))]]) ).

thf(8,plain,
    ! [A: n] :
      ( ( c_plus @ A @ c0 )
      = A ),
    inference(cnf,[status(esa)],[3]) ).

thf(14,plain,
    ! [A: n] :
      ( ( c_plus @ A @ c0 )
      = A ),
    inference(lifteq,[status(thm)],[8]) ).

thf(6,plain,
    ! [B: n,A: n] :
      ( ( c_plus @ A @ ( cS @ B ) )
      = ( cS @ ( c_plus @ A @ B ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(10,plain,
    ! [B: n,A: n] :
      ( ( c_plus @ A @ ( cS @ B ) )
      = ( cS @ ( c_plus @ A @ B ) ) ),
    inference(lifteq,[status(thm)],[6]) ).

thf(11,plain,
    ! [B: n,A: n] :
      ( ( c_plus @ A @ ( cS @ B ) )
      = ( cS @ ( c_plus @ A @ B ) ) ),
    inference(simp,[status(thm)],[10]) ).

thf(19,plain,
    ( ( c_plus @ c0 @ sk2 )
   != sk2 ),
    inference(rewrite,[status(thm)],[9,14]) ).

thf(134,plain,
    ! [B: n,A: n] :
      ( ( ( cS @ ( c_plus @ A @ B ) )
       != sk2 )
      | ( ( c_plus @ A @ ( cS @ B ) )
       != ( c_plus @ c0 @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[11,19]) ).

thf(163,plain,
    ! [B: n,A: n] :
      ( ( ( cS @ ( c_plus @ A @ B ) )
       != sk2 )
      | ( A != c0 )
      | ( ( cS @ B )
       != sk2 ) ),
    inference(simp,[status(thm)],[134]) ).

thf(172,plain,
    ! [A: n] :
      ( ( ( cS @ ( c_plus @ c0 @ A ) )
       != sk2 )
      | ( ( cS @ A )
       != sk2 ) ),
    inference(simp,[status(thm)],[163]) ).

thf(187,plain,
    ! [B: n,A: n] :
      ( ( ( cS @ A )
       != sk2 )
      | ( ( cS @ B )
       != sk2 )
      | ( ( c_plus @ A @ c0 )
       != ( c_plus @ c0 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[14,172]) ).

thf(188,plain,
    ( ( ( cS @ c0 )
     != sk2 )
    | ( ( cS @ c0 )
     != sk2 ) ),
    inference(pattern_uni,[status(thm)],[187:[bind(A,$thf( c0 )),bind(B,$thf( c0 ))]]) ).

thf(247,plain,
    ( ( cS @ c0 )
   != sk2 ),
    inference(simp,[status(thm)],[188]) ).

thf(328,plain,
    ! [C: n,B: n > n,A: n > n] :
      ( ( ( A @ c0 )
       != ( B @ c0 ) )
      | ( ( A @ ( sk1 @ B @ A ) )
        = ( B @ ( sk1 @ B @ A ) ) )
      | ( ( B @ C )
       != c0 )
      | ( ( A @ C )
       != sk2 ) ),
    inference(paramod_ordered,[status(thm)],[16,18]) ).

thf(500,plain,
    ! [A: n > n] :
      ( ( ( A @ c0 )
       != c0 )
      | ( ( A
          @ ( sk1 @ A
            @ ^ [B: n] : B ) )
        = ( sk1 @ A
          @ ^ [B: n] : B ) )
      | ( ( A @ sk2 )
       != c0 ) ),
    inference(pre_uni,[status(thm)],[328:[bind(A,$thf( ^ [D: n] : D )),bind(B,$thf( B )),bind(C,$thf( sk2 ))]]) ).

thf(501,plain,
    ( ( sk1
      @ ^ [A: n] : c0
      @ ^ [A: n] : A )
    = c0 ),
    inference(pre_uni,[status(thm)],[500:[bind(A,$thf( ^ [B: n] : c0 ))]]) ).

thf(7,plain,
    ! [C: n,B: n > n,A: n > n] :
      ( ( ( A @ c0 )
       != ( B @ c0 ) )
      | ( ( A @ ( cS @ ( sk1 @ B @ A ) ) )
       != ( B @ ( cS @ ( sk1 @ B @ A ) ) ) )
      | ( ( A @ C )
        = ( B @ C ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(12,plain,
    ! [C: n,B: n > n,A: n > n] :
      ( ( ( A @ c0 )
       != ( B @ c0 ) )
      | ( ( A @ ( cS @ ( sk1 @ B @ A ) ) )
       != ( B @ ( cS @ ( sk1 @ B @ A ) ) ) )
      | ( ( A @ C )
        = ( B @ C ) ) ),
    inference(lifteq,[status(thm)],[7]) ).

thf(13,plain,
    ! [C: n,B: n > n,A: n > n] :
      ( ( ( A @ c0 )
       != ( B @ c0 ) )
      | ( ( A @ ( cS @ ( sk1 @ B @ A ) ) )
       != ( B @ ( cS @ ( sk1 @ B @ A ) ) ) )
      | ( ( A @ C )
        = ( B @ C ) ) ),
    inference(simp,[status(thm)],[12]) ).

thf(27,plain,
    ! [C: n,B: n > n,A: n > n] :
      ( ( ( A @ c0 )
       != ( B @ c0 ) )
      | ( ( A @ ( cS @ ( sk1 @ B @ A ) ) )
       != ( B @ ( cS @ ( sk1 @ B @ A ) ) ) )
      | ( ( A @ C )
       != c0 )
      | ( ( B @ C )
       != sk2 ) ),
    inference(paramod_ordered,[status(thm)],[13,18]) ).

thf(47,plain,
    ! [A: n > n] :
      ( ( ( A @ c0 )
       != c0 )
      | ( ( A
          @ ( cS
            @ ( sk1
              @ ^ [B: n] : B
              @ A ) ) )
       != ( cS
          @ ( sk1
            @ ^ [B: n] : B
            @ A ) ) )
      | ( ( A @ sk2 )
       != c0 ) ),
    inference(pre_uni,[status(thm)],[27:[bind(A,$thf( A )),bind(B,$thf( ^ [D: n] : D )),bind(C,$thf( sk2 ))]]) ).

thf(2723,plain,
    ! [A: n > n] :
      ( ( ( A
          @ ( cS
            @ ( sk1
              @ ^ [B: n] : B
              @ A ) ) )
       != ( cS
          @ ( sk1
            @ ^ [B: n] : B
            @ A ) ) )
      | ( ( A @ sk2 )
       != c0 )
      | ( ( sk1
          @ ^ [B: n] : B
          @ ^ [B: n] : c0 )
       != ( A @ c0 ) ) ),
    inference(paramod_ordered,[status(thm)],[481,47]) ).

thf(2824,plain,
    ( ( ( sk1
        @ ^ [A: n] : A
        @ ^ [A: n] :
            ( cS
            @ ( sk1
              @ ^ [B: n] : B
              @ ^ [B: n] :
                  ( sk1
                  @ ^ [C: n] : C
                  @ ^ [C: n] : B ) ) ) )
     != ( cS
        @ ( sk1
          @ ^ [A: n] : A
          @ ^ [A: n] :
              ( sk1
              @ ^ [B: n] : B
              @ ^ [B: n] : A ) ) ) )
    | ( ( sk1
        @ ^ [A: n] : A
        @ ^ [A: n] : sk2 )
     != c0 ) ),
    inference(pre_uni,[status(thm)],[2723:[bind(A,$thf( ^ [B: n] : ( sk1 @ ^ [C: n] : C @ ^ [C: n] : B ) ))]]) ).

thf(4384,plain,
    ( ( ( sk1
        @ ^ [A: n] : A
        @ ^ [A: n] :
            ( cS
            @ ( sk1
              @ ^ [B: n] : B
              @ ^ [B: n] :
                  ( sk1
                  @ ^ [C: n] : C
                  @ ^ [C: n] : B ) ) ) )
     != ( cS
        @ ( sk1
          @ ^ [A: n] : A
          @ ^ [A: n] :
              ( sk1
              @ ^ [B: n] : B
              @ ^ [B: n] : A ) ) ) )
    | ( ( sk1
        @ ^ [A: n] : c0
        @ ^ [A: n] : A )
     != ( sk1
        @ ^ [A: n] : A
        @ ^ [A: n] : sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[501,2824]) ).

thf(4423,plain,
    ( ( ( sk1
        @ ^ [A: n] : A
        @ ^ [A: n] :
            ( cS
            @ ( sk1
              @ ^ [B: n] : B
              @ ^ [B: n] :
                  ( sk1
                  @ ^ [C: n] : C
                  @ ^ [C: n] : B ) ) ) )
     != ( cS
        @ ( sk1
          @ ^ [A: n] : A
          @ ^ [A: n] :
              ( sk1
              @ ^ [B: n] : B
              @ ^ [B: n] : A ) ) ) )
    | ( ( ^ [A: n] : c0 )
     != ( ^ [A: n] : A ) )
    | ( ( ^ [A: n] : A )
     != ( ^ [A: n] : sk2 ) ) ),
    inference(simp,[status(thm)],[4384]) ).

thf(5293,plain,
    ( ( ( sk1
        @ ^ [A: n] : A
        @ ^ [A: n] : ( cS @ c0 ) )
     != ( cS
        @ ( sk1
          @ ^ [A: n] : A
          @ ^ [A: n] :
              ( sk1
              @ ^ [B: n] : B
              @ ^ [B: n] : A ) ) ) )
    | ( ( ^ [A: n] : c0 )
     != ( ^ [A: n] : A ) )
    | ( ( ^ [A: n] : A )
     != ( ^ [A: n] : sk2 ) )
    | ( ( sk1
        @ ^ [A: n] : c0
        @ ^ [A: n] : A )
     != ( sk1
        @ ^ [A: n] : A
        @ ^ [A: n] :
            ( sk1
            @ ^ [B: n] : B
            @ ^ [B: n] : A ) ) ) ),
    inference(paramod_ordered,[status(thm)],[501,4423]) ).

thf(5368,plain,
    ( ( ( sk1
        @ ^ [A: n] : A
        @ ^ [A: n] : ( cS @ c0 ) )
     != ( cS
        @ ( sk1
          @ ^ [A: n] : A
          @ ^ [A: n] :
              ( sk1
              @ ^ [B: n] : B
              @ ^ [B: n] : A ) ) ) )
    | ( ( ^ [A: n] : c0 )
     != ( ^ [A: n] : A ) )
    | ( ( ^ [A: n] : A )
     != ( ^ [A: n] : sk2 ) )
    | ( ( ^ [A: n] : c0 )
     != ( ^ [A: n] : A ) )
    | ( ( ^ [A: n] :
            ( sk1
            @ ^ [B: n] : B
            @ ^ [B: n] : A ) )
     != ( ^ [A: n] : A ) ) ),
    inference(simp,[status(thm)],[5293]) ).

thf(5424,plain,
    ( ( ( sk1
        @ ^ [A: n] : A
        @ ^ [A: n] : ( cS @ c0 ) )
     != ( cS
        @ ( sk1
          @ ^ [A: n] : A
          @ ^ [A: n] :
              ( sk1
              @ ^ [B: n] : B
              @ ^ [B: n] : A ) ) ) )
    | ( ( ^ [A: n] : c0 )
     != ( ^ [A: n] : A ) )
    | ( ( ^ [A: n] : A )
     != ( ^ [A: n] : sk2 ) )
    | ( ( ^ [A: n] :
            ( sk1
            @ ^ [B: n] : B
            @ ^ [B: n] : A ) )
     != ( ^ [A: n] : A ) ) ),
    inference(simp,[status(thm)],[5368]) ).

thf(5722,plain,
    ( ( ( sk1
        @ ^ [A: n] : A
        @ ^ [A: n] : ( cS @ c0 ) )
     != ( cS @ c0 ) )
    | ( ( ^ [A: n] : c0 )
     != ( ^ [A: n] : A ) )
    | ( ( ^ [A: n] : A )
     != ( ^ [A: n] : sk2 ) )
    | ( ( ^ [A: n] :
            ( sk1
            @ ^ [B: n] : B
            @ ^ [B: n] : A ) )
     != ( ^ [A: n] : A ) )
    | ( ( sk1
        @ ^ [A: n] : c0
        @ ^ [A: n] : A )
     != ( sk1
        @ ^ [A: n] : A
        @ ^ [A: n] :
            ( sk1
            @ ^ [B: n] : B
            @ ^ [B: n] : A ) ) ) ),
    inference(paramod_ordered,[status(thm)],[501,5424]) ).

thf(5795,plain,
    ( ( ( sk1
        @ ^ [A: n] : A
        @ ^ [A: n] : ( cS @ c0 ) )
     != ( cS @ c0 ) )
    | ( ( ^ [A: n] : c0 )
     != ( ^ [A: n] : A ) )
    | ( ( ^ [A: n] : A )
     != ( ^ [A: n] : sk2 ) )
    | ( ( ^ [A: n] :
            ( sk1
            @ ^ [B: n] : B
            @ ^ [B: n] : A ) )
     != ( ^ [A: n] : A ) )
    | ( ( ^ [A: n] : c0 )
     != ( ^ [A: n] : A ) )
    | ( ( ^ [A: n] :
            ( sk1
            @ ^ [B: n] : B
            @ ^ [B: n] : A ) )
     != ( ^ [A: n] : A ) ) ),
    inference(simp,[status(thm)],[5722]) ).

thf(5906,plain,
    ( ( ( sk1
        @ ^ [A: n] : A
        @ ^ [A: n] : ( cS @ c0 ) )
     != ( cS @ c0 ) )
    | ( ( ^ [A: n] : c0 )
     != ( ^ [A: n] : A ) )
    | ( ( ^ [A: n] : A )
     != ( ^ [A: n] : sk2 ) )
    | ( ( ^ [A: n] :
            ( sk1
            @ ^ [B: n] : B
            @ ^ [B: n] : A ) )
     != ( ^ [A: n] : A ) ) ),
    inference(simp,[status(thm)],[5795]) ).

thf(197,plain,
    ! [C: n,B: n,A: n] :
      ( ( ( cS @ ( cS @ ( c_plus @ A @ B ) ) )
       != sk2 )
      | ( ( cS @ C )
       != sk2 )
      | ( ( c_plus @ A @ ( cS @ B ) )
       != ( c_plus @ c0 @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[11,172]) ).

thf(198,plain,
    ! [A: n] :
      ( ( ( cS @ ( cS @ ( c_plus @ c0 @ A ) ) )
       != sk2 )
      | ( ( cS @ ( cS @ A ) )
       != sk2 ) ),
    inference(pattern_uni,[status(thm)],[197:[bind(A,$thf( c0 )),bind(B,$thf( D )),bind(C,$thf( cS @ D ))]]) ).

thf(224,plain,
    ! [A: n] :
      ( ( ( cS @ ( cS @ ( c_plus @ c0 @ A ) ) )
       != sk2 )
      | ( ( cS @ ( cS @ A ) )
       != sk2 ) ),
    inference(simp,[status(thm)],[198]) ).

thf(1216,plain,
    ! [C: n,B: n,A: n] :
      ( ( ( cS @ ( cS @ ( cS @ ( c_plus @ A @ B ) ) ) )
       != sk2 )
      | ( ( cS @ ( cS @ C ) )
       != sk2 )
      | ( ( c_plus @ A @ ( cS @ B ) )
       != ( c_plus @ c0 @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[11,224]) ).

thf(1217,plain,
    ! [A: n] :
      ( ( ( cS @ ( cS @ ( cS @ ( c_plus @ c0 @ A ) ) ) )
       != sk2 )
      | ( ( cS @ ( cS @ ( cS @ A ) ) )
       != sk2 ) ),
    inference(pattern_uni,[status(thm)],[1216:[bind(A,$thf( c0 )),bind(B,$thf( D )),bind(C,$thf( cS @ D ))]]) ).

thf(1329,plain,
    ! [A: n] :
      ( ( ( cS @ ( cS @ ( cS @ ( c_plus @ c0 @ A ) ) ) )
       != sk2 )
      | ( ( cS @ ( cS @ ( cS @ A ) ) )
       != sk2 ) ),
    inference(simp,[status(thm)],[1217]) ).

thf(2125,plain,
    ! [B: n,A: n] :
      ( ( ( cS @ ( cS @ ( cS @ A ) ) )
       != sk2 )
      | ( ( cS @ ( cS @ ( cS @ B ) ) )
       != sk2 )
      | ( ( c_plus @ A @ c0 )
       != ( c_plus @ c0 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[14,1329]) ).

thf(2126,plain,
    ( ( ( cS @ ( cS @ ( cS @ c0 ) ) )
     != sk2 )
    | ( ( cS @ ( cS @ ( cS @ c0 ) ) )
     != sk2 ) ),
    inference(pattern_uni,[status(thm)],[2125:[bind(A,$thf( c0 )),bind(B,$thf( c0 ))]]) ).

thf(2432,plain,
    ( ( cS @ ( cS @ ( cS @ c0 ) ) )
   != sk2 ),
    inference(simp,[status(thm)],[2126]) ).

thf(1178,plain,
    ! [B: n,A: n] :
      ( ( ( cS @ ( cS @ A ) )
       != sk2 )
      | ( ( cS @ ( cS @ B ) )
       != sk2 )
      | ( ( c_plus @ A @ c0 )
       != ( c_plus @ c0 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[14,224]) ).

thf(1179,plain,
    ( ( ( cS @ ( cS @ c0 ) )
     != sk2 )
    | ( ( cS @ ( cS @ c0 ) )
     != sk2 ) ),
    inference(pattern_uni,[status(thm)],[1178:[bind(A,$thf( c0 )),bind(B,$thf( c0 ))]]) ).

thf(1328,plain,
    ( ( cS @ ( cS @ c0 ) )
   != sk2 ),
    inference(simp,[status(thm)],[1179]) ).

thf(41,plain,
    ! [C: n,B: n > n,A: n > n] :
      ( ( ( A @ c0 )
       != ( B @ c0 ) )
      | ( ( A @ C )
        = ( B @ C ) )
      | ( ( A @ ( cS @ ( sk1 @ B @ A ) ) )
       != ( B @ c0 ) )
      | ( ( B @ ( cS @ ( sk1 @ B @ A ) ) )
       != ( A @ c0 ) ) ),
    inference(eqfactor_ordered,[status(thm)],[13]) ).

thf(44,plain,
    ! [C: n,B: n > n,A: n > n] :
      ( ( ( A @ c0 )
       != ( B @ c0 ) )
      | ( ( A @ C )
        = ( B @ C ) )
      | ( ( A @ ( cS @ ( sk1 @ B @ A ) ) )
       != ( B @ c0 ) )
      | ( ( B @ ( cS @ ( sk1 @ B @ A ) ) )
       != ( A @ c0 ) ) ),
    inference(pre_uni,[status(thm)],[41:[]]) ).

thf(45,plain,
    ! [C: n,B: n > n,A: n > n] :
      ( ( ( A @ C )
        = ( B @ C ) )
      | ( ( A @ c0 )
       != ( B @ c0 ) )
      | ( ( A @ ( cS @ ( sk1 @ B @ A ) ) )
       != ( B @ c0 ) )
      | ( ( B @ ( cS @ ( sk1 @ B @ A ) ) )
       != ( A @ c0 ) ) ),
    inference(pre_uni,[status(thm)],[44:[]]) ).

thf(4341,plain,
    ( ( ( sk1
        @ ^ [A: n] : A
        @ ^ [A: n] :
            ( cS
            @ ( sk1
              @ ^ [B: n] : B
              @ ^ [B: n] :
                  ( sk1
                  @ ^ [C: n] : C
                  @ ^ [C: n] : B ) ) ) )
     != ( cS
        @ ( sk1
          @ ^ [A: n] : A
          @ ^ [A: n] :
              ( sk1
              @ ^ [B: n] : B
              @ ^ [B: n] : A ) ) ) )
    | ( ( sk1
        @ ^ [A: n] : A
        @ ^ [A: n] : sk2 )
     != ( sk1
        @ ^ [A: n] : A
        @ ^ [A: n] : c0 ) ) ),
    inference(paramod_ordered,[status(thm)],[481,2824]) ).

thf(4436,plain,
    ( ( ( sk1
        @ ^ [A: n] : A
        @ ^ [A: n] :
            ( cS
            @ ( sk1
              @ ^ [B: n] : B
              @ ^ [B: n] :
                  ( sk1
                  @ ^ [C: n] : C
                  @ ^ [C: n] : B ) ) ) )
     != ( cS
        @ ( sk1
          @ ^ [A: n] : A
          @ ^ [A: n] :
              ( sk1
              @ ^ [B: n] : B
              @ ^ [B: n] : A ) ) ) )
    | ( ( ^ [A: n] : A )
     != ( ^ [A: n] : A ) )
    | ( ( ^ [A: n] : sk2 )
     != ( ^ [A: n] : c0 ) ) ),
    inference(simp,[status(thm)],[4341]) ).

thf(4505,plain,
    ( ( ( sk1
        @ ^ [A: n] : A
        @ ^ [A: n] :
            ( cS
            @ ( sk1
              @ ^ [B: n] : B
              @ ^ [B: n] :
                  ( sk1
                  @ ^ [C: n] : C
                  @ ^ [C: n] : B ) ) ) )
     != ( cS
        @ ( sk1
          @ ^ [A: n] : A
          @ ^ [A: n] :
              ( sk1
              @ ^ [B: n] : B
              @ ^ [B: n] : A ) ) ) )
    | ( ( ^ [A: n] : sk2 )
     != ( ^ [A: n] : c0 ) ) ),
    inference(simp,[status(thm)],[4436]) ).

thf(199,plain,
    ! [A: n] :
      ( ( ( cS @ A )
       != sk2 )
      | ( ( cS @ ( c_plus @ c0 @ A ) )
       != ( cS @ A ) )
      | ( sk2 != sk2 ) ),
    inference(eqfactor_ordered,[status(thm)],[172]) ).

thf(218,plain,
    ! [A: n] :
      ( ( ( cS @ A )
       != sk2 )
      | ( ( c_plus @ c0 @ A )
       != A ) ),
    inference(simp,[status(thm)],[199]) ).

thf(31,plain,
    ! [C: n,B: n > n,A: n > n] :
      ( ( ( A @ c0 )
       != ( B @ c0 ) )
      | ( ( A @ ( cS @ ( sk1 @ B @ A ) ) )
       != ( B @ ( cS @ ( sk1 @ B @ A ) ) ) )
      | ( ( A @ C )
       != sk2 )
      | ( ( B @ C )
       != ( c_plus @ c0 @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[13,19]) ).

thf(58,plain,
    ! [A: n > n] :
      ( ( ( A @ c0 )
       != c0 )
      | ( ( A
          @ ( cS
            @ ( sk1
              @ ^ [B: n] : B
              @ A ) ) )
       != ( cS
          @ ( sk1
            @ ^ [B: n] : B
            @ A ) ) )
      | ( ( A @ ( c_plus @ c0 @ sk2 ) )
       != sk2 ) ),
    inference(pre_uni,[status(thm)],[31:[bind(A,$thf( A )),bind(B,$thf( ^ [D: n] : D )),bind(C,$thf( c_plus @ c0 @ sk2 ))]]) ).

thf(32,plain,
    ! [C: n,B: n > n,A: n > n] :
      ( ( ( A @ c0 )
       != ( B @ c0 ) )
      | ( ( A @ ( cS @ ( sk1 @ B @ A ) ) )
       != ( B @ ( cS @ ( sk1 @ B @ A ) ) ) )
      | ( ( c_plus @ ( A @ C ) @ sk2 )
       != sk2 )
      | ( ( B @ C )
       != c0 ) ),
    inference(paramod_ordered,[status(thm)],[13,19]) ).

thf(79,plain,
    ! [A: n > n] :
      ( ( ( A @ c0 )
       != c0 )
      | ( ( A
          @ ( cS
            @ ( sk1
              @ ^ [B: n] : B
              @ A ) ) )
       != ( cS
          @ ( sk1
            @ ^ [B: n] : B
            @ A ) ) )
      | ( ( c_plus @ ( A @ c0 ) @ sk2 )
       != sk2 ) ),
    inference(pre_uni,[status(thm)],[32:[bind(A,$thf( A )),bind(B,$thf( ^ [D: n] : D )),bind(C,$thf( c0 ))]]) ).

thf(2792,plain,
    ! [A: n > n] :
      ( ( ( A @ c0 )
       != c0 )
      | ( ( cS
          @ ( sk1
            @ ^ [B: n] : B
            @ A ) )
       != c0 )
      | ( ( A @ sk2 )
       != c0 )
      | ( ( sk1
          @ ^ [B: n] : c0
          @ ^ [B: n] : B )
       != ( A
          @ ( cS
            @ ( sk1
              @ ^ [B: n] : B
              @ A ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[501,47]) ).

thf(2887,plain,
    ( ( ( sk1
        @ ^ [A: n] : c0
        @ ^ [A: n] : A )
     != c0 )
    | ( ( cS
        @ ( sk1
          @ ^ [A: n] : A
          @ ^ [A: n] :
              ( sk1
              @ ^ [B: n] : c0
              @ ^ [B: n] : B ) ) )
     != c0 )
    | ( ( sk1
        @ ^ [A: n] : c0
        @ ^ [A: n] : A )
     != c0 ) ),
    inference(pre_uni,[status(thm)],[2792:[bind(A,$thf( ^ [B: n] : ( sk1 @ ^ [C: n] : c0 @ ^ [C: n] : C ) ))]]) ).

thf(2951,plain,
    ( ( ( sk1
        @ ^ [A: n] : c0
        @ ^ [A: n] : A )
     != c0 )
    | ( ( cS
        @ ( sk1
          @ ^ [A: n] : A
          @ ^ [A: n] :
              ( sk1
              @ ^ [B: n] : c0
              @ ^ [B: n] : B ) ) )
     != c0 ) ),
    inference(simp,[status(thm)],[2887]) ).

thf(3060,plain,
    ( ( c0 != c0 )
    | ( ( cS
        @ ( sk1
          @ ^ [A: n] : A
          @ ^ [A: n] : c0 ) )
     != c0 ) ),
    inference(rewrite,[status(thm)],[2951,501]) ).

thf(3061,plain,
    ( ( cS
      @ ( sk1
        @ ^ [A: n] : A
        @ ^ [A: n] : c0 ) )
   != c0 ),
    inference(simp,[status(thm)],[3060]) ).

thf(2790,plain,
    ! [A: n > n] :
      ( ( ( A
          @ ( cS
            @ ( sk1
              @ ^ [B: n] : B
              @ A ) ) )
       != ( cS
          @ ( sk1
            @ ^ [B: n] : B
            @ A ) ) )
      | ( ( A @ sk2 )
       != c0 )
      | ( ( sk1
          @ ^ [B: n] : c0
          @ ^ [B: n] : B )
       != ( A @ c0 ) ) ),
    inference(paramod_ordered,[status(thm)],[501,47]) ).

thf(2845,plain,
    ( ( ( sk1
        @ ^ [A: n] :
            ( cS
            @ ( sk1
              @ ^ [B: n] : B
              @ ^ [B: n] :
                  ( sk1
                  @ ^ [C: n] : B
                  @ ^ [C: n] : C ) ) )
        @ ^ [A: n] : A )
     != ( cS
        @ ( sk1
          @ ^ [A: n] : A
          @ ^ [A: n] :
              ( sk1
              @ ^ [B: n] : A
              @ ^ [B: n] : B ) ) ) )
    | ( ( sk1
        @ ^ [A: n] : sk2
        @ ^ [A: n] : A )
     != c0 ) ),
    inference(pre_uni,[status(thm)],[2790:[bind(A,$thf( ^ [B: n] : ( sk1 @ ^ [C: n] : B @ ^ [C: n] : C ) ))]]) ).

thf(6336,plain,
    ( ( ( sk1
        @ ^ [A: n] :
            ( cS
            @ ( sk1
              @ ^ [B: n] : B
              @ ^ [B: n] :
                  ( sk1
                  @ ^ [C: n] : B
                  @ ^ [C: n] : C ) ) )
        @ ^ [A: n] : A )
     != ( cS
        @ ( sk1
          @ ^ [A: n] : A
          @ ^ [A: n] :
              ( sk1
              @ ^ [B: n] : A
              @ ^ [B: n] : B ) ) ) )
    | ( ( sk1
        @ ^ [A: n] : sk2
        @ ^ [A: n] : A )
     != ( sk1
        @ ^ [A: n] : c0
        @ ^ [A: n] : A ) ) ),
    inference(paramod_ordered,[status(thm)],[501,2845]) ).

thf(6339,plain,
    ( ( ( sk1
        @ ^ [A: n] :
            ( cS
            @ ( sk1
              @ ^ [B: n] : B
              @ ^ [B: n] :
                  ( sk1
                  @ ^ [C: n] : B
                  @ ^ [C: n] : C ) ) )
        @ ^ [A: n] : A )
     != ( cS
        @ ( sk1
          @ ^ [A: n] : A
          @ ^ [A: n] :
              ( sk1
              @ ^ [B: n] : A
              @ ^ [B: n] : B ) ) ) )
    | ( ( ^ [A: n] : sk2 )
     != ( ^ [A: n] : c0 ) )
    | ( ( ^ [A: n] : A )
     != ( ^ [A: n] : A ) ) ),
    inference(simp,[status(thm)],[6336]) ).

thf(6434,plain,
    ( ( ( sk1
        @ ^ [A: n] :
            ( cS
            @ ( sk1
              @ ^ [B: n] : B
              @ ^ [B: n] :
                  ( sk1
                  @ ^ [C: n] : B
                  @ ^ [C: n] : C ) ) )
        @ ^ [A: n] : A )
     != ( cS
        @ ( sk1
          @ ^ [A: n] : A
          @ ^ [A: n] :
              ( sk1
              @ ^ [B: n] : A
              @ ^ [B: n] : B ) ) ) )
    | ( ( ^ [A: n] : sk2 )
     != ( ^ [A: n] : c0 ) ) ),
    inference(simp,[status(thm)],[6339]) ).

thf(60,plain,
    ! [A: n > n] :
      ( ( ( A @ c0 )
       != ( c_plus @ c0 @ sk2 ) )
      | ( ( A
          @ ( cS
            @ ( sk1
              @ ^ [B: n] : ( c_plus @ B @ sk2 )
              @ A ) ) )
       != ( c_plus
          @ ( cS
            @ ( sk1
              @ ^ [B: n] : ( c_plus @ B @ sk2 )
              @ A ) )
          @ sk2 ) )
      | ( ( A @ c0 )
       != sk2 ) ),
    inference(pre_uni,[status(thm)],[31:[bind(A,$thf( A )),bind(B,$thf( ^ [D: n] : ( c_plus @ D @ sk2 ) )),bind(C,$thf( c0 ))]]) ).

thf(5294,plain,
    ( ( ( cS
        @ ( sk1
          @ ^ [A: n] : A
          @ ^ [A: n] :
              ( sk1
              @ ^ [B: n] : B
              @ ^ [B: n] : A ) ) )
     != c0 )
    | ( ( ^ [A: n] : c0 )
     != ( ^ [A: n] : A ) )
    | ( ( ^ [A: n] : A )
     != ( ^ [A: n] : sk2 ) )
    | ( ( sk1
        @ ^ [A: n] : c0
        @ ^ [A: n] : A )
     != ( sk1
        @ ^ [A: n] : A
        @ ^ [A: n] :
            ( cS
            @ ( sk1
              @ ^ [B: n] : B
              @ ^ [B: n] :
                  ( sk1
                  @ ^ [C: n] : C
                  @ ^ [C: n] : B ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[501,4423]) ).

thf(5349,plain,
    ( ( ( cS
        @ ( sk1
          @ ^ [A: n] : A
          @ ^ [A: n] :
              ( sk1
              @ ^ [B: n] : B
              @ ^ [B: n] : A ) ) )
     != c0 )
    | ( ( ^ [A: n] : c0 )
     != ( ^ [A: n] : A ) )
    | ( ( ^ [A: n] : A )
     != ( ^ [A: n] : sk2 ) )
    | ( ( ^ [A: n] : c0 )
     != ( ^ [A: n] : A ) )
    | ( ( ^ [A: n] :
            ( cS
            @ ( sk1
              @ ^ [B: n] : B
              @ ^ [B: n] :
                  ( sk1
                  @ ^ [C: n] : C
                  @ ^ [C: n] : B ) ) ) )
     != ( ^ [A: n] : A ) ) ),
    inference(simp,[status(thm)],[5294]) ).

thf(5411,plain,
    ( ( ( cS
        @ ( sk1
          @ ^ [A: n] : A
          @ ^ [A: n] :
              ( sk1
              @ ^ [B: n] : B
              @ ^ [B: n] : A ) ) )
     != c0 )
    | ( ( ^ [A: n] : c0 )
     != ( ^ [A: n] : A ) )
    | ( ( ^ [A: n] : A )
     != ( ^ [A: n] : sk2 ) )
    | ( ( ^ [A: n] :
            ( cS
            @ ( sk1
              @ ^ [B: n] : B
              @ ^ [B: n] :
                  ( sk1
                  @ ^ [C: n] : C
                  @ ^ [C: n] : B ) ) ) )
     != ( ^ [A: n] : A ) ) ),
    inference(simp,[status(thm)],[5349]) ).

thf(33,plain,
    ! [C: n,B: n > n,A: n > n] :
      ( ( ( A @ c0 )
       != ( B @ c0 ) )
      | ( ( A @ ( cS @ ( sk1 @ B @ A ) ) )
       != ( B @ ( cS @ ( sk1 @ B @ A ) ) ) )
      | ( ( c_plus @ c0 @ ( A @ C ) )
       != sk2 )
      | ( ( B @ C )
       != sk2 ) ),
    inference(paramod_ordered,[status(thm)],[13,19]) ).

thf(67,plain,
    ! [A: n > n] :
      ( ( ( A @ c0 )
       != c0 )
      | ( ( A
          @ ( cS
            @ ( sk1
              @ ^ [B: n] : B
              @ A ) ) )
       != ( cS
          @ ( sk1
            @ ^ [B: n] : B
            @ A ) ) )
      | ( ( c_plus @ c0 @ ( A @ sk2 ) )
       != sk2 ) ),
    inference(pre_uni,[status(thm)],[33:[bind(A,$thf( A )),bind(B,$thf( ^ [D: n] : D )),bind(C,$thf( sk2 ))]]) ).

thf(2724,plain,
    ! [A: n > n] :
      ( ( ( A @ c0 )
       != c0 )
      | ( ( A @ ( cS @ c0 ) )
       != ( cS
          @ ( sk1
            @ ^ [B: n] : B
            @ A ) ) )
      | ( ( A @ sk2 )
       != c0 )
      | ( ( sk1
          @ ^ [B: n] : B
          @ ^ [B: n] : c0 )
       != ( sk1
          @ ^ [B: n] : B
          @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[481,47]) ).

thf(2725,plain,
    ( ( c0 != c0 )
    | ( ( cS
        @ ( sk1
          @ ^ [A: n] : A
          @ ^ [A: n] : c0 ) )
     != c0 )
    | ( c0 != c0 ) ),
    inference(pattern_uni,[status(thm)],[2724:[bind(A,$thf( ^ [B: n] : c0 ))]]) ).

thf(2964,plain,
    ( ( cS
      @ ( sk1
        @ ^ [A: n] : A
        @ ^ [A: n] : c0 ) )
   != c0 ),
    inference(simp,[status(thm)],[2725]) ).

thf(2983,plain,
    ( ( cS @ c0 )
   != c0 ),
    inference(rewrite,[status(thm)],[2964,481]) ).

thf(856,plain,
    ! [C: n,B: n > n,A: n > n] :
      ( ( ( A @ c0 )
       != ( B @ c0 ) )
      | ( ( A @ C )
        = ( B @ C ) )
      | ( ( A @ ( sk1 @ B @ A ) )
        = c0 )
      | ( ( B @ ( sk1 @ B @ A ) )
       != ( sk1
          @ ^ [D: n] : D
          @ ^ [D: n] : c0 ) ) ),
    inference(paramod_ordered,[status(thm)],[16,481]) ).

thf(895,plain,
    ! [B: n,A: n > n] :
      ( ( ( A @ c0 )
       != ( sk1
          @ ^ [C: n] : C
          @ ^ [C: n] : c0 ) )
      | ( ( A @ B )
        = ( sk1
          @ ^ [C: n] : C
          @ ^ [C: n] : c0 ) )
      | ( ( A
          @ ( sk1
            @ ^ [C: n] :
                ( sk1
                @ ^ [D: n] : D
                @ ^ [D: n] : c0 )
            @ A ) )
        = c0 ) ),
    inference(pre_uni,[status(thm)],[856:[bind(A,$thf( A )),bind(B,$thf( ^ [D: n] : ( sk1 @ ^ [E: n] : E @ ^ [E: n] : c0 ) )),bind(C,$thf( C ))]]) ).

thf(898,plain,
    ! [A: n] :
      ( ( ( sk1
          @ ^ [B: n] : B
          @ ^ [B: n] :
              ( sk1
              @ ^ [C: n] :
                  ( sk1
                  @ ^ [D: n] : D
                  @ ^ [D: n] : c0 )
              @ ^ [C: n] :
                  ( sk1
                  @ ^ [D: n] : D
                  @ ^ [D: n] : C ) ) )
        = c0 )
      | ( ( sk1
          @ ^ [B: n] : B
          @ ^ [B: n] : A )
        = ( sk1
          @ ^ [B: n] : B
          @ ^ [B: n] : c0 ) ) ),
    inference(pre_uni,[status(thm)],[895:[bind(A,$thf( ^ [C: n] : ( sk1 @ ^ [D: n] : D @ ^ [D: n] : C ) )),bind(B,$thf( B ))]]) ).

thf(966,plain,
    ! [A: n] :
      ( ( ( sk1
          @ ^ [B: n] : B
          @ ^ [B: n] :
              ( sk1
              @ ^ [C: n] :
                  ( sk1
                  @ ^ [D: n] : D
                  @ ^ [D: n] : c0 )
              @ ^ [C: n] :
                  ( sk1
                  @ ^ [D: n] : D
                  @ ^ [D: n] : C ) ) )
        = c0 )
      | ( ( sk1
          @ ^ [B: n] : B
          @ ^ [B: n] : A )
        = ( sk1
          @ ^ [B: n] : B
          @ ^ [B: n] : c0 ) ) ),
    inference(simp,[status(thm)],[898]) ).

thf(6820,plain,
    ! [A: n] :
      ( ( ( sk1
          @ ^ [B: n] : B
          @ ^ [B: n] :
              ( sk1
              @ ^ [C: n] : c0
              @ ^ [C: n] :
                  ( sk1
                  @ ^ [D: n] : D
                  @ ^ [D: n] : C ) ) )
        = c0 )
      | ( ( sk1
          @ ^ [B: n] : B
          @ ^ [B: n] : A )
        = c0 ) ),
    inference(rewrite,[status(thm)],[966,481]) ).

thf(6907,plain,
    ! [A: n] :
      ( ( ( sk1
          @ ^ [B: n] : B
          @ ^ [B: n] : A )
        = c0 )
      | ( ( sk1
          @ ^ [B: n] : B
          @ ^ [B: n] :
              ( sk1
              @ ^ [C: n] : c0
              @ ^ [C: n] :
                  ( sk1
                  @ ^ [D: n] : D
                  @ ^ [D: n] : C ) ) )
       != ( sk1
          @ ^ [B: n] : B
          @ ^ [B: n] : A ) )
      | ( c0 != c0 ) ),
    inference(eqfactor_ordered,[status(thm)],[6820]) ).

thf(6911,plain,
    ( ( sk1
      @ ^ [A: n] : A
      @ ^ [A: n] :
          ( sk1
          @ ^ [B: n] : c0
          @ ^ [B: n] :
              ( sk1
              @ ^ [C: n] : C
              @ ^ [C: n] : B ) ) )
    = c0 ),
    inference(pattern_uni,[status(thm)],[6907:[bind(A,$thf( sk1 @ ^ [B: n] : c0 @ ^ [B: n] : ( sk1 @ ^ [C: n] : C @ ^ [C: n] : B ) ))]]) ).

thf(61,plain,
    ! [A: n > n] :
      ( ( ( A @ c0 )
       != ( c_plus @ c0 @ c0 ) )
      | ( ( A @ ( cS @ ( sk1 @ ( c_plus @ c0 ) @ A ) ) )
       != ( c_plus @ c0 @ ( cS @ ( sk1 @ ( c_plus @ c0 ) @ A ) ) ) )
      | ( ( A @ sk2 )
       != sk2 ) ),
    inference(pre_uni,[status(thm)],[31:[bind(A,$thf( A )),bind(B,$thf( c_plus @ c0 )),bind(C,$thf( sk2 ))]]) ).

thf(4533,plain,
    ! [A: n > n] :
      ( ( ( A @ c0 )
       != c0 )
      | ( ( A @ ( cS @ ( sk1 @ ( c_plus @ c0 ) @ A ) ) )
       != ( cS @ ( c_plus @ c0 @ ( sk1 @ ( c_plus @ c0 ) @ A ) ) ) )
      | ( ( A @ sk2 )
       != sk2 ) ),
    inference(rewrite,[status(thm)],[61,11,14]) ).

thf(9799,plain,
    $false,
    inference(e,[status(thm)],[481,247,5906,2432,224,1328,1329,45,4505,172,2824,3,5424,18,11,218,58,79,14,3061,6434,60,5411,2845,13,67,16,2983,19,47,6911,501,4533,4423]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : NUM827^5 : TPTP v8.1.2. Bugfixed v5.3.0.
% 0.12/0.16  % Command  : run_Leo-III %s %d
% 0.15/0.37  % Computer : n002.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Mon May  6 12:32:54 EDT 2024
% 0.15/0.37  % CPUTime  : 
% 1.07/0.94  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.19/1.08  % [INFO] 	 Parsing done (135ms). 
% 1.45/1.09  % [INFO] 	 Running in sequential loop mode. 
% 1.87/1.33  % [INFO] 	 eprover registered as external prover. 
% 1.87/1.33  % [INFO] 	 cvc4 registered as external prover. 
% 1.87/1.34  % [INFO] 	 Scanning for conjecture ... 
% 2.05/1.41  % [INFO] 	 Found a conjecture and 0 axioms. Running axiom selection ... 
% 2.05/1.44  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.05/1.44  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.05/1.44  % [INFO] 	 Type checking passed. 
% 2.05/1.45  % [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 ... 
% 43.77/9.54  % External prover 'e' found a proof!
% 43.77/9.54  % [INFO] 	 Killing All external provers ... 
% 43.77/9.54  % Time passed: 8999ms (effective reasoning time: 8448ms)
% 43.77/9.54  % 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)>
% 43.77/9.55  % Axioms used in derivation (0): 
% 43.77/9.55  % No. of inferences in proof: 97
% 43.77/9.55  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 8999 ms resp. 8448 ms w/o parsing
% 43.77/9.61  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 43.77/9.61  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------